Influence of temperature on protein binding and decay rates
Let's do your second one first, you want to find the rate of binding:

Yes you are right you need to calculate for km

I think I found the paper that ties temp into the reaction rate:

statistical approach called response surface methodology (RSM) is used for the prediction of the kinetic constants of glucose oxidase (GOx) as a function of reaction temperature and pH. Lineweaver–Burk transformation of the Michaelis–Menten equation was utilized as the integral part of the RSM algorithm. The effects of variables, namely reciprocal of substrate concentration (0.033–0.5 mM−1), reaction temperature (14.9–40.1 °C) and reaction pH (pH 4.4–8.5) on the reciprocal of initial reaction rate were evaluated and a second order polynomial model was fitted by a central composite circumscribed design (CCCD).

Biochemical Engineering Journal
August 2005, Vol.25(1):55–62, doi:10.1016/j.bej.2005.04.001
A new approach for determination of enzyme kinetic constants using response surface methodology
İsmail Hakkı Boyacı

For the decay

I'm still working on the first I'm suggesting to check this out but need sleep I can read it tomorrow

http://www.eastcoastbio.com/productcart/pc/stability_testing.asp