The ideal temperature at which to study the effect of proteases on protein is 37°C. Why are higher temperatures not advisable?

Likely because of 2 things:

1. The protease is not active at a temperature higher than 37C

2. The protein (s) you are studying to be degraded by the protease may be denatured and then the protease may not work because the structure is messed up of the protein (s) it is targeting.