Originally posted by @uzless
Seems on the quantum level an object can have different temperatures at the same time.
Oh Heizenburg....90 years later and you're still frustrating us. Not only is the cat both alive and dead, it's now hot and cold!
I'm in two minds about this. On the one hand the article you referenced quotes one of the authors of the paper talking about energy uncertainty in the thermometer
, which isn't the same as the system whose temperature being measured being in a linear superposition of temperatures. So I'm not certain if the journalist hasn't got hold of the wrong end of the stick. Unfortunately the link in the article referenced in the OP is broken so I couldn't look at the actual paper. One issue is that the statistical physics definition of temperature has it defined in terms of the gradient of the density of states function. So temperature is a function of energy. But that does not entitle one to claim it should be indefinite just because the energy is. My understanding of the definition is that the "input" variable is the energy expectation value and it's not clear this will lead to a linear superposition. The Heisenberg uncertainty principle has two variables, only one of which can be known exactly. In technical terms the quantum operators do not commute.
However, on the other hand, in finite temperature quantum field theory temperature replaces time. So one would expect, instead of energy time uncertainty, energy temperature uncertainty. This, however, jars somewhat with the considerations of the previous paragraph as the temperature and energy should be "knowable" at the same time.
So I'd have to read the paper to form an opinion.