The "heat" leaves the planet constantly as radiated energy. The radiated energy that heats the planet is all, but an infinitesimal amount, arriving constantly from the Sun.
The Earth radiates heat. Look up black body radiation.
The atmosphere reduces the rate at which heat leaves the planet (amongst a few other things). It is a complex picture, but a number of the elements that make up the atmosphere have different effects on the rate of heat dispersion. Water vapour has the greatest effect but it is not alone. Small changes in the amount of other atmospheric elements have the effect of changing the rate of dispersion which is in a rough equilibrium.
An example that is easy to follow is to pick a station in a desert and observe the difference between maximum and minimum temperatures in any 24 hour period. Compare it to a coastal station at roughly the same latitude. The rate differs greatly between the stations.
The atmosphere varies greatly in its composition both horizontally and vertically. Therefore to measure the effect, you have to sample many points simultaneously and then use extrapolation and statistics to get an idea of what is happening globally.
It can be argued that the atmosphere is the greatest part of that which keeps the earth average temperature at approx 15 deg C. By changing the makeup of the atmosphere you can move that average up or down.
Reversing the calculations to predict what will happen at one of the locations that data was sampled from, if the average was to change slightly, is as near as impossible a task as trying to explain facebook to a group of mini-goats gambolling around a peak in the Alps.
The first part is hard enough but the concept of accurate predictions of change is harder. Not impossible to predict more broad effects but not easy.