Question

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

Answer 1

The heat given to a substance without changing its temperature but its state is called latent heat.

Answer 2

yes, we can give heat to substance without raising its temperature and this is possible with the help of latent heat of fusion.
Latent heat convert ice into liquid without change its temperature.For example-ice and water both have 0 degree temperature.