The heating and cooling rates for PWHT are nonessential welding variables. You can edit the WPS to reflect what the cooling rates should be. For example,the heating and cooling rates shall not exeed 200 deg c/hr.

Some construction Codes have limits on heating and cooling rates. You can and should also specify those requirements in your WPS.

Significant thermal stresses or overheats can occur in some specific cases, related to heating rates.

For a thick walled ( > 100 mm thk) vessel a > 100C/hr heatup rate may develop thermal stresses in excess of yield , and this would not be habit-forming.

For butt welds that are being heat by heating coils spaced more than 150 mm from the weld and for which thermocouples were not placed directly under the heating coils then a fast heat up rate can overtemper the pipe section directly under the heating coils. See PP presentations by Superheat corp.

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick

Heating and cooling rates are more about retaining structural integrity (i.e., distortion) than about stress relief or metallurgy.
When the component includes different thicknesses, use multiple thermocouples.
For some structures it is wise not to use the maximum permitted rates.

"If you don't have time to do the job right the first time, when are you going to find time to repair it?"