Look friends! Temperature totally depends on the Internal Energy. It is quite untrue that addition of heat will necessarily increase the temperature of the system under study. If heat energy is supplied it can be counter balanced by an equal amount of work being done by the system! It's just like you receive cash from one hand and then you spend an equal amount from your savings leading to no net profit.
The temperature of a body is a measure of it's total internal energy and nothing else ! The temperature of a system can be varied due to heat exchange or due to work being done on or being done by the system.
One example is that suppose we heat a container of gas (the container has a movable lid). Then the gas molecules expand against the external pressure and may end up doing an equivalent amount of work as the supplied heat energy. Hence in the end the gas did not gain any energy! So, the temperature did not change despite the fact that heat was supplied to the system!