A number of people here are equating weight and mass.
These are not the same.
Mass is, roughly, the amount of 'stuff' something has, how hard it is to change somethings velocity.
Weight is the downward force of an object, caused by gravity and after mitigating factors (i.e. bouyancy)
It is not clear whether you meant weight or mass in the question, however an object is usually referred to as heavier if it weighs more, so I think it more likely you meant weight.
While a hotter object will have more energy, and thus due to mass-energy equivalence wll have more mass, a hotter object is also (usually) less dense. This lower density means that it takes up a larger volume, leading to a larger bouyant force and therefore reduced weight, despite the increased mass.
The effect of the reduced density is usually much larger than the increased energy, since the mass increase due to relativity is tiny. The equation, after all, is E = mc^2, so the mass increases with Ec^-2. Since c = 300000000 approx., this increase is incredibly small.