The thermal capacity of the chamber C and the objects contained and the heating time t are the basis of the calculation.

C (in J/K) is the sum of the thermal capacities of all materials. For each material the thermal capacity Ci is the product of its mass and its specific therml capacity of the material itself. The specific thermal capacity is 1000 J/kg K for most materials, the exsception being 4180 J/kg·K for water and about 2000 J/kg·K for woodend materials or wet materials

The needed power is the C (Tf-Ti)/t where Ti and Tf are the initial and final temperatures.

The air has also a specific thermal capacity of 1000 J/kg·K so the power brought by the air is 1000·M(Tin - Tc) where M is the mass floor rate in kg/s, Tin is the inlet air temperature and Tc the air temperature is the room, startin at Ti and ending at Tf.

The exact solution needs to solve a differential equation, but a first approximation can be obtained by putting Tc = (Tf-Ti)/2 and equating the needed power and the power brought by the air.

what temperature you are looking for?

1. Select the temperature- required for the material.

2 Use heat and mass transfer equation to estimate the flow. (using specific heat of fluid such as carbon, nitrogen, oxygen)

3. find the pump of requirement and integrate it with a thermocouple.

4. Design an algorithm of the cooling curve which you are looking for.

such as linear cooling, exponential cooling, Two-way surface cooling for radial curvature.

Please free to ask how to set up this device?

I am assuming that you are interested in accurate accurate parameters and thus it is not prudent to ignore losses and other factors because you may end up with inaccurate air flow and inaccurate temperatures assuming that you may. For example the viscosity and other properties of of air are bound to сhange with temperature because of the bimolecular nitrogen and oxygen. However, if you are okay with 5% error, then you could use standard equations and ignore losses.