Raising the temperature of the air would generally reduce the relative humidity (RH), all else being equal, i.e., you warmed the air without adding undue amounts of water vapour through, for example, hanging wet washing, boiling lots of vegetables, etc. Lower RH leads to the wood drying further, although the effect is gradual because wood does not release its bonded moisture easily: nor for that matter does it adsorb additional moisture instantly or especially quickly when it's placed in a more humid atmosphere, although quickly in this case is both a relative and rather vague or unspecific term.
Regarding the shrinkage that occurred in your construction you have to look at the width of the piece of wood drying and shrinking. Let's say that you experience 5% shrinkage across the width - I'm not going to start complicating matters by discussing the difference between radial and tangential shrinkage/expansion of different wood species. Then say that your piece of wood is 10 mm wide and shrinks 5% as it dries. This piece will finish up at 9.5 mm wide. Now take a piece of wood of the same species 100 mm wide that shrinks by 5%, and it ends up 95 mm wide. Now relate that information to the situation you have, i.e., a piece of wood that is essentially a segment of a circle, wide at one end and tapering to 0 or nothing at the other. Next, put enough of those segments together to make a circle (your table top) and extrapolate the end result from that using the information I've just provided.
I haven't even touched on the opposite condition, the expansion of dry wood across the grain as it adsorbs moisture, and nor am I going to complicate matters by discussing such things as the non-linear expansion and contraction rates of wood from Fibre Saturation Point (FSP) to the condition known as oven dry, nor get into hysteresis and other such exotica. Slainte.
