It depends on the size of the satellite and its power use. Small spacecraft often don't use enough power to generate enough heat to warm themselves. The problem then is batteries get cold (which is one of the places you need heaters) and become inefficient and then you end up in death spiral. Here the probe likely wasn't generating enough power anyway, so that would almost certainly kill it before the cold.
The problem is less the quantity of heat generated than of shedding that heat. Even modest electronics emit several watts of thermal waste heat, and given that the entire satellite is in a highly-insulating vacuum, as well as subject to solar insolation (at 1 kW/m²), it's easy to exceed thermal budgets.
You can do the sums. Spacecraft lose heat by radiation and if you do the sums for a small spacecraft you can see the equilibrium temperature is low enough that you don't need to take any special measures to shed the heat.
