Change in internal energy= change in work doneBut if change in heat energy should cause change in temperature but it is not happening why?

Change in internal energy= change in work done

this is the case in case of adiabatic process.

Change in heat energy= change in internal energy + change in work done

This is the thermodynamics 1^stlaw and different possibilities exist depends upon the process being carried out.

Change in heat energy = change in internal energy (Isochoric Process)
Change in internal energy is actually the change in tempearature. Hence it is possible.