woah...lots of factors involved but you can get a basic idea
for black powder the combustion gas temp is 3307 degrees
you have to divide this number by a constant (R)
the constant for black powder is 22.16 per foot
or 1.846 per inch
so if you wanted to know the(theoretical) temp say 6" from the charge you would multiply 6(inches) X 1.846....=11.076
divide the combustion gas temp 3307 by 11.076...
= 298 degrees,,but you would have to factor in the volume of the chamber,diameter of charge ...ect .but you can be sure that the temp will be no higher than these calculations
These equations assume the gas temperature is 3307 R and are used to predict the peak pressure obtained when a certain weight of BP are burned in a given volume. A temperature of 3307 R is about 2850 F or 1564 C. That hot.
Calculating the gas temperature during the gas expansion is far more complicated and requires solving a bunch of time dependent differential equations to get an accurate answer. Ted's equations don't touch that aspect of the problem.
When you go through the equations describing the chemistry of the BP decomposition, you will find that 1 gram of BP generates about 120 cubic inches of hot gas at the combustion temperature and atmospheric pressure which will fill the parachute compartment and damage or melt an unprotected parachute. After the gas cools to room temperature the volume is 20 cubic inches, a factor of 6 reduction to the the lower temperature.
Baffles, wadding and chute protectors preventing hot particles from impinging on a chute and by providing surface area to cool the gas.