I know you think I'm an old fool, perhaps you're right but, I'll risk offering a reply:
"Is it over the top?"
Just as a semiconductor malfunctions at too high a temperature, it can likewise malfunction at too low a temperature and there was a thread on here recently saying just that.
What you want, if you are going to those lengths, is temperature control, not just cooling. You need a system that will maintain the operating conditions at the optimum for the particular device. This is a lot more than just cooling and if you are going to the lengths of doing something like this, it would be best to do it properly.
Modern semiconductors are much more heat tolerant than they used to be. I remember years ago working with GaAs diode infra red detectors that only functioned at the temperature of boiling liquid nitrogen. Anything above that they acted like a piece of wire and conducted the same in both directions. At a lower temp, they were insulators and didn't conduct anything.