I know poders have differant burn rates but do differant powders run cooler for more frequent shooting?
This will be for a .243 sporter and my next purchase of either a .223 or 22-250 in heavy barrel.

I posed a similar question to the people at Hodgdon powders years ago. Their response was that their ball powder's burns at a lower temperature than their extruded powders. My results seem to concur with this.

I believe TBS is correct. Various powders do have different temps. However, I don't believe the temperature variations are of much consequence to normal shooters.

ALL powders burn way beyond the melting point of steel. Fortunately this inferno is only roaring down the barrel for a fraction of a second.

I think where engineers and metalurgist suddenly got interested in burning rates and temperatures was for military purposes and trying to design better powders and barrels to extend the life of machine gun barrels. Ball powders seemed to be the least abraisive on barrels in machine guns. Thus I think all military small arms ammunition today is loaded with various ball powders. (Someone please correct me if I am wrong in this statement.)

Again, for the average shooter it's likely a moot subject.