In experimental thermodynamic bench experiments, those who are familiar with boiling water in a common scientific vessel such as a tea kettle, are often familiar with how a system has its own characteristic rate of cooling, depending on the energy of the heated media to dissipate into whatever heat exchange facility is available at the time, usually ambient convection.
Under careful observation it can be seen that often it is possible to impart energy from an external source at a faster rate than the same amount of energy will later require to completely dissipate afterward.
People shouldn't be discouraged whether this is obvious or not.
Experimentation such as this can require quite a bit of dedication, especially among those who are not tea drinkers, but this is the workaround that would be required to arrive at such valid conclusions without the use of equations nor those pesky optical tweezers which are such a pain in the butt.
The incentive structures you hint at don’t make sense either.
Most people will say “yes”, but dialetheists [1] (or at least some of them) will disagree. Since I’m not certain those dialetheists are wrong, I can’t be certain the events of the story are impossible (I have no trouble saying they are astronomically unlikely, but impossibility and astronomical unlikelihood are strictly speaking distinct)
[0] https://projecteuclid.org/journals/notre-dame-journal-of-for...