LeafByNiggle:
“Not introducing those uncertainties in the first place” means discarding all the measurements with uncertainties, which leaves you with maximum uncertainty, as uncertainty is the lack of knowledge. “Some” uncertainty is better than “maximum” uncertainty.
That’s not actually applicable in this case. There is one number (temperature) that is a combination of measurements and calculations (not quite guesswork, but certainly containing best guess estimates). There is a second number (heat content) that is purely calculation, based on estimates of various constants multiplied by the temperature. Which number contains fewer estimates, the one with X estimates or the one with X + Y estimates? Which number is more likely to be accurate, the one with more uncertainties or the one with less?