Consider the following two statements.

A)    If heat is added to a system, its temperature must increase.

B)    If positive work is done by a system in a thermodynamic process, its volume must increase.

On addition of heat, the temperature will increase only if internal energy increases.

If the work done by gas has more magnitude than given heat then even on supplying heat, internal energy decreases. Hence, the temperature decreases.

For the gas to do positive work it must expand.