This is, I think, my point. The wideband noise racket (currents) is associated with the DC dark current, and gets bigger with bigger dark currents, which get bigger with temperature, but that wideband noise is not the same thing as the DC dark current. Knowing that we can see a noise floor lower that what comes out of a reverse biased diode, I think we can have this gadget work as well as any at the kind of workshop temperatures most of us would tolerate on a hot day.
BUT..
I do have one of those "flat" heat pipes about15mm wide, and 3mm thick. If simply put in there, as if it was part of the EM shielding, one might put the end of the heatpipe sticking out of the machine into a glass of ice.
I don't think we will need to go for cooling, but there is easily the potential to accommodate it.
Mark - thanks much for the Id equation. I know I have it somewhere, but that was handy.