That last answer is slightly confused. By Charle's law (called Gay-Lussac's Law in France), V1/T1=V2/T2 at constant pressure, where Vs are volume and Ts are temperature. Therefore, if one increases the temperature T1 >T2, then one would expect the volume to increase as well, so V1>V2.
However, this is assuming equal pressure. Obviously, as the temperature of the balloon increases, one might expect the pressure to increase as well. This situation is governed by the universal gas law, PV=nRT, and as temperature T increases, one would expect the product PV to increase as well, probably some increase in pressure P and some increase in volume V, depending on how stretchy the balloon is. Another factor that comes into play is that balloons are permeable, so as the pressure increases, more gas inside the balloon will diffuse out of the balloon, decreasing the volume of the balloon.
I would expect that over a short period, the balloon would expand from the heating of the gas inside, but over a longer period, the heat and pressure would encourage enhanced diffusion, causing the ballooon to shrink.
In cold water, obviously diffusion will not operate as efficiently, and one will have a more straightforward application of the universal gas law, so that the product PV will decrease with decreasing temperature over both the short and long terms.
The rate at which the heated balloon contracts due to loss of air inside by diffusion depends on the permeability of the balloon surface.