Yeah I feared it was going to be hard for you to make the connection most layman don't get it because here on earth it's hard to initially see whats happening because of out atmosphere and sun.
Ok so lets teleport you and you screen instantly out into deep space a point a long way from a sun. So you arrive and you start cooling rapidly to around 4 degrees above absolute zero the temperature in deep space and then when you finally get to 4 degree and then you start cooling with the universe. Think about why do you cool you aren't in contact with anything and convection doesn't work in a vacuum.
So the connection is temperature contains information and all objects radiate that information. If that wasn't true you wouldn't and couldn't cool in the situation in space because you are not in contact with anything to transfer heat with by normal convection methods.
Do you see the connection now the process is happening when you are sitting there on earth but you and your monitor are also gaining information or energy from your surroundings.
Now we still haven't got to the bottom of the real issue does measurement itself cost energy and in 1961 as we started to develop the microprocessor this became important and so it was an IBM engineer put forward an idea
Landauers principle So now even heat is starting to look a bit different under QM than under classic physics and what we have is the energy cost of measurement is the work energy of the acquired information. So basically all observation/measurement looks exactly the same as the heat example, the one we are most familiar with and that is what Haroche’s experiment showed. It also shows you QM has to obey all the standard energy laws from classic physics even though it can break many classic physic rules.
As a sort of funny aside ending to this you may want to consider the energy information value you carry in your head and you then undertook time travel back in time
