My wife and I are having an "ongoing household discussion". She claims that it is bad to place hot food in the fridge, because it causes the fridge to work harder. I claim the impact is negligible. Neither of us have data to back up our claims.
To her point, yes the fridge must "work harder" since it is a closed-loop system trying to maintain a temperature set point, and the introduction of a hot body with decent thermal inertia must cause it to spend longer on whatever it does to whisk away heat.
However, the difference of "Hot" food and "Warm" food is probably 30 degrees (F), from 90 to 60F, and the fridge probably has a set point of roughly 40F. I assumed those first 20-30 deg cooling happen rapidly, and the last 20-30 happens much slower, due to the exponential solution to the heat equation.
Finally, neither of us know whether the primary source of fridge failure is wear from cooling or other factors, so we don't even know if the "cooling activation" properties are relevant.