Assuming that you speak about the time constant (thermal inertia is the mass x heat capacity), you must minimize the heat transfer efficiency.

This can be done by modifying the shape to minimize the total surface area (sphere). Convection might alter the optimal shape from a sphere to a flatter structure.

@ Abhishek, thanks for the update.

but thermal conductivity is constant for a material right. for that matter thermal conductivity, density and specific heat all are material properties, how does material property change with area. 

@ Yvan, thanks for the info.

Ya I am taking about time constant literally. curved surface has higher area than flat one, right. And also increasing area increases the heat transfer thereby decreasing time constant. 

Can you break the block in many pieces and join together. This may add additional thermal resistance and restrict heat release/increase thereby increasing thermal inertia?

@Satish, thanks for the info.

@Abhishek, thanks for the update.

But I still don't understand the physic how the material property change with geometry. Are you talking about effective thermal conductivity or the individual conductivity. 

Maybe you should also try restricting heat conduction inside the material itself by having internal voids/thermal barrier walls  either filled with some sort of insulating material or if you are material sensitive then just voids with air

@Antonis, thanks for the update.

I think heat treatment will improve the thermal inertia of material

@ Rakesh, thanks for the info.

Can you throw a better light. May any reference, pdf......etc.....

But, wouldn't it alter  the material. Or are you talking about surface hardening techniques.

Hi Rajesh, thermal inertia is done by specific heat capacity of the material. So the only way how to increase the intertia (and keeping the geometry the same) is to change the specific heat. And thus very likely only a molecular structure (maybe). In other words, you have to put hands in molecular (atomic) structure. What could maybe help, is to operate your piece in higher temperature range. But this applies to specific heat by mass.

On the other hand, if you increase dimensions of your piece ( and thus mass) you can increase the total heat capacity, just because you increase the mass. 

So you can play with specific heat (but on the molecualr basis) and/or with the total mass and thus with the total heat capacity. 

If you can alter your piece in a more substantial way, you can put in it some encapsulated PCM (Phase change material) that can dramatically increase the inertia. Keep in mind that  you look for something that reduces temperature changes and thus PCM might be one option. 

@Miroslav, thanks for the update.

By the way Rajesh, if it is not a proprietary information, what is the application you look for? It might be a good example for my students in Heat transfer course.

The following informaton may be useful for your studeis 

The thermal inertia of a material is defined as the square root of the product of the material's bulk thermal conductivity and volumetric heat capacity, where the latter is the product of density and specific heat capacity:

I=Thermal inertia ={k rho cp} ^0.5

thermal ineria  can be changed  with variation of k, which depends on material and 

temperature. Since material is not to be changed (as per g iven data), increase bulik temperature of body, which affects k

Once temperature is changed, there will be change in density and specific heat (marginal effect) Increase of volume of the body with change of dimensions also affect density (as density is ratio of mass to volume) and  specific heat.   

Rajesh it might be worth recapping that Thermal diffusivity (α) is a closely related property to thermal mass or thermal inertia and describes the rate at which heat is transferred through the cross sectional depth of a material. Thermal diffusivity (m2/s) is calculated by dividing the thermal conductivity(k) of a material (W/mK) by the volumetric specific heat capacity (at a constant pressure), α= k/(Cp.ρ ).

Thus assuming that you cannot alter the shape or volume of your material, the only options open to you are to reduce the conductivity of the material (e.g typically achieved by studying the temperature dependent conductivity of the particular material or increasing the thermal resistance of the material by modifying its structure). Alternatively increasing the materials density and/or specific heat capacity. Thus without physically altering the chemical composition or build-up of the material your only option would be to increase the density of it. Additionally if you are able to apply a surface coating then you could look at ways to lower the surface transfer coefficient  through increasing the surface resistivity or take advatage of phase change properties by adding a PC coating, as already suggested above.

@Maddali sir, thanks for the info.

@ Robert, thanks for the info.

Low thermal conductivity, High specific heat and high mass. All these increase the thermal inertia,

.

@ Mahmoud, thanks for the update.

Ya, but how to increase it practically, without altering the material.

Thermal inertia is a phisical property of a material, such as mass. You may ask for increasing thermal inertia of a body, but not a material.

@ Ali, thanks for the info. Ya, that is right.

Note that your question should be re-phrased to be: "How to change the thermal inertia of a certain amount of a material, not a material" 

The thermal inertia of a certain amount of mass depends on the mass and the specific heat of the material. If you can not change the material, then you can not change the specific heat (unless you change the temperature causing the specific heat to change). The only thing you can do is to change the mass by changing the dimensions of your system to hold more mass. 

@ Abdul, thanks for the info.

@ Abhishek, thanks for the update.

Actually, from the comments from all researchers I think one need to play with mass to alter the thermal inertia.

The perceived inertia depends on the material mass (m), specific heat (Cp) and eventually of the latent heat of melting (or vaporization) (L) if the working temperature is similar to the phase change temperature. So, depending of the material melting (or vaporization temperature) and the system operating temperature, the perceived inertia my be quite different, namely because the latent component (m.L) is usually quite large when compared with the so called sensible component  (m.Cp)

Nelson is right. Check the material phase diagram and subject the material to various pressures to bring the phase change temperature to whatever temperature you want your inertia to work.

Nelson is right. But this solution is limited to very special condition considering aplicable range of tempreture.

@Nelson, thanks for the info.

@Daniel, thanks for the update.

@Ali, thanks for the update.

without having more details i am not sure what application you are considering. the thermal inertia will depend on the amount of heat stored in the system to the amount of heat loss from the system. hence,mass, thermal conductivity, exposed area  and heat trasnfer coefficient are the main parameters to consider. reducing the mass will reduce the amount of heat stored (can you use a porous structure to reduce the mass). can the heat transfer coefficent be increased to accelerate heat loss.

Heat inertia is a reason of difference between the rate of heat consuption/production and the value of signal output at heat-flux DSC or DTA. This heat inertia is proportional to the sum of two heat capacities: of the sample and of the sample holder. Saving dimensions of sample you can change dimension or material of sample holder.  

@Pavel, thanks for the update.

@Boukhanouf, thanks for the info.

Rajesh - without knowing the exact application it is difficult to say but if you could tell us which inertia properties , e.g decrement factor, decrement delay are more important to you and also whether there is a particular attenuation time step involved that would help. Short of embedding PCMs (which would obviously alter the material composition) you are limited but by increasing the effective surface area you will increase the rate of convective heat transfer