If the hot side is in contact with a thermal mass, even a heatsink, there won't be much thermal shock on the wafer.
Project is to control temperature of a heat-producing device, a solid heatsink makes sense.
Within a Peltier, the heat travels between the junctions as electron states in current not as molecular movement. The heat is taken up by electrons crossing from the more highly conductive material on one side of the junction to the less highly conductive material (heat raises electrons above the step) and then heat is released when those electrons cross back to the first material and lose the excess energy. Between junctions the energy transferred is not heating the material between, Seebeck knew this first!
The semiconductors don't get hot except through much slower conduction from the hot side. That is my concern about thermal stress, would cycling power cause an appreciable fast temperature drop in the wafer. Mostly ever not.
I agree that smoothing power to the wafer should be best but not about necessity. A low-bypass filter with components able to take the wattage, how much there?