Heat transfer is the transfer of thermal energy from a body, at a high temperature, to another at a lower temperature. This transfer of thermal energy may occur under steady or unsteady state conditions. Under Steady state conditions the temperature within the system does not change with time. Conversely, under unsteady state conditions the temperature within the system does vary with time.
Unsteady state conditions are a precursor to steady state conditions. No system exists initially under steady state conditions. Some time must pass, after heat transfer is initiated, before the system reaches steady state. During that period of transition the system is under unsteady state conditions.
Clearly, no system can remain under unsteady state conditions perpetually. The temperature of the system will eventually reach the temperature of the heat source, and once this happens, the system will be at steady state. Even if the amount of heat being transferred into the system is increased, at some point the system reaches its critical temperature and the energy transferred into it the starts causing phase changes within the system rather than temperatures increases.