Question

under what conditions heat can be given to a substance without raising its temperature ?

Answer 1

When the substance is at its boiling or melting point, heat can be given to it without raising it's temperature. This is so because the heat supplied is used in changing the phase of the substance (liquid to gas or solid to liquid) and there isn't a change in its temperature.

Answer 2

Heat can be given to a substance without raising its temperature,When a substance is changing its physical state[for eg from solid to liquid and liquid to gas ].
The heat energy which has to be supplied to change the state of substance is called its Latent Heat.
Latent heat  does not raise the temperature . But Latent heat must be supplied to  change the state of substance.

Note : The word " Latent" means HEAT is HIDDEN in the substances undergoing the state change.