Heating of mixture of gases with one gas barely above its boiling point
You could certainly have such a situation; that is, heating two compounds in their gaseous state at constant volume such that that the total pressure of the system exceeds the vapor pressure of the lower boiling compound causing it to condense.  

As the gas condenses, it will of course give off heat as you said, but it would require continued heat input to sustain the increasing pressure and condensation. I believe that is what you meant in your second question anyway.