Well seeing as I'm measuring the initial rate of temperature change (i.e. the rate an infinitesimal amount of time after the beginning of the reaction) things like specific heat should still have the same value as before the reaction. Though of course in practice I can't just work out the rate...
In a chemical investigation I'm currently undertaking as part of a chemistry course I'm am studying I'm recording how the temperature changes in several reactions and using the rate of temperature change as a measure of the rate of reaction. I believe this is a valid way to do it as you...