There are at least two different aspects of the problem you need to consider: power dissipation and timing.
- higher clock rate means higher switching frequencies, thus greater power dissipation.
If your design has overheating problems, then a lower clock rate could indeed improve the situation.
- change in temperature will slightly affect timing. If your design has a critical timing,
it could fail if the temperature (or supply, or any other parameter) approaches the specified limit.
In such cases a lower clock rate could or could not solve the problem. This depends on the
reason a path is not meeting timing: as a rule of thumb, if you have critical timing on setup, reducing
frequency makes sense; not if you have hold problems.
