I would say no. Heating a liquid does introduce energy into the cylinder and energy is really a form of mass (and the other way around), but you'd need a lot of energy to see it on a scale. And I mean a lot of energy.
The heated cylinder would expand, which due to buoyancy might cause it to be a little bit "lighter" according to the scale. You'd probably need a hell of a scale to pick this up.
There would be movement of air around the cylinder due to convection. I suppose that could also be picked up depending on the scale.
In any case, the actual weight of the cylinder would be unchanged neglecting relativistic effects.