If an object's average radiated power is different from its average absorbed power, its temperature must change. Think of energy in minus energy out.
If an object radiates less power than it absorbs, it gains energy each second, so its internal energy increases and its temperature rises. If it radiates more power than it absorbs, it loses energy each second and its temperature falls. A cup of hot tea in a cool room radiates more than it absorbs, so it cools. A cold car bonnet in morning sunshine absorbs more than it radiates, so it warms up.
The change does not go on for ever. As an object warms, it emits a greater intensity, so the power it radiates increases. Eventually the radiated power rises to match the absorbed power and the temperature levels off at a new constant value. In the same way, a cooling object radiates less as it cools until the two powers balance again.