It seems to me like there's some assumptions you're making in your essentially linear approximation of peak black-body radiation intensity over time that I'm not knowledgeable enough to be able to judge as to validity, but your reasoning don't seem obviously wrong.
Also the resolving power in terms of dynamic range of JWST's image sensors is another issue; it seems to me that that would have a bearing on your theory. I'm not sure that a distant object just a few degrees above the 105°K temperature limit would stand out from the background enough for the JWST sensors to get much of a read on it. I suppose if they integrate light for many weeks or months (like they did for the Hubble Deep Field pictures) they could get enough signal-to-noise ratio to resolve such an object.
Oh, please! Not even "back-of-the-envelope" calculations! Just "spit-balling" here! For "ordinary" solid objects located in a uniform environment having a different temperature, Newton's Temperature Law would apply - meaning: logarithmic cooling. My talking about the temperature halving with every doubling of age was just a ballpark estimate.
I'm not sure that a distant object just a few degrees above the 105°K temperature limit would stand out from the background enough for the JWST sensors to get much of a read on it.
Again: No "degree" sign for Kelvin. The unit is "Kelvin," not "degrees Kelvin."
I suppose if they integrate light for many weeks or months (like they did for the Hubble Deep Field pictures) they could get enough signal-to-noise ratio to resolve such an object.
Again: Just "spit-balling" here, but I would think that a more than 100 Kelvin difference would be more than sufficient.
Regards,