The Stefan Boltzmann law describes how a body emits heat radiatively and cools down. If radiative heat transfer is the most important heat transfer process, you can use this to model your system. Anyway, the short answer is that the cooling rate is proportional to the fourth power of the temperature. However, you do need to consider the environment too.

Hi Abhijit Banik .....cooling rate do not effect the geometry and size of the metallic ( pure and bimetallic) objects especially Pd, Pt, Cu, Au, Fe

At the peak temp. if its difference is more than surrounding, the rate of coolinging is more and as temp. decreases the cooling rate falls  

Dear Abhijit Banik

Your question is for general metals. The peak temp. depend on the type of metal, but the  rate of cooling  if it is fast(is called quenching) this effect on crystalline arrangement  and the metallic object become more hardening   that is different if the rate of cooling is slowly, in this case is called heat treatment(annealing) and the crystal becomes more arrangement contains less of defects, more crystalline growth .   

Prof. Mustafa, Could you please provide any resource to read more about this?

Thank you

Cooling rate dT/dt, isn't?

so temperature (T) difference within certain time (t) difference will define the cooling rate. 

So

faster cooling rate, if there is a large Temperature difference in a very short time.

while slow cooling rate will tend to occur in a longer time difference for the same Temp difference.

Thus time difference is affecting more on cooling rate, than the peak of temperature.

Dear  Mohammed Shurrab

These processes include peak temp. and cooling rate are  principals for heat treatments obtained from any resources , papers  or thesis's.Thanks

Dear Joy Rizki Pangestu Djuansjah

Your comments is very correct,  but there are two principle cases affect on metallic materials related to peak temp. and cooling rate( atomic arrangement, crystal growth,crystal defects,  ect.)First: heat treatment e,g.put the material in oven ( 450 C at 2 hr.) and make the material gradually cooling at room temp..second : put the material in oven ( 450 C at 2 hr.) and put the material directly in cooling liquid(shrinking for material)is called quenching(Sudden cooling)Thanks

With best regards   

Thank you very much.

Sorry for my mistake . 

If peak temperature is meant by the peak in DTA

May be this will help:

https://www.researchgate.net/post/What_does_the_DTA_differential_thermal_analysis_peak_height_imply_What_about_sharpness_of_a_peak