The temperature of an object is seen to increase over a certain...

According to the first law of thermodynamics, $\Delta Q = \Delta U + \Delta W$, where $\Delta Q$ is the heat supplied to the system, $\Delta U$ is the change in internal energy, and $\Delta W$ is the work done by the system.

An increase in temperature indicates an increase in the internal energy of the object ($\Delta U > 0$).

From the first law, $\Delta U$ can be positive if heat is supplied to the object ($\Delta Q > 0$) or if work is done on the object ($\Delta W < 0$), or both.

Thus, work might have been done on the object, or heat might have been supplied to it. It is not necessary that heat is definitely supplied, as the temperature can increase adiabatically by doing work on the object alone.