Firstly, there is no such thing as polyester epoxy. It's either polyester or epoxy. They are two completely different chemistries. Although heating can speed up the cure time, if you're casting a large volume of either resin, it can get too hot which leads to cracks and bubbles in the resin.
Epoxy has a tendency to stick to some silicon rubber moulds so that when you demould your casting, it brings small pieces of mould with it. Polyester resin can stay tacky after it's cured due either to contamination with moisture in the atmosphere or due to the styrene in it soaking into the silicon rubber. In the worst cases, the silicon rubber mould can expand and distort if the absorption is high. Rinsing the resulting cast in cellulose thinner can remove the sticky surface. The silicon mould will more or less return to normal if you let it breath for a couple of days.
The worst problem about the tackiness is that Polyester resin shrinks quite noticeably. It tends to pull away from the mould and if the resin surface against the mould is not cured properly (which often happens), the surface is spoilt. Heating either resin can encourage shrinkage. If you put your mould somewhere merely warm and dry, I'd stick to the recommended curing times on the pack. There's a reason they're formulated to take a long time to cure. It's to give air bubbles a chance to rise, to keep shrinkage at a minimum and reduce the chance of runaway exothermic reaction occuring which will promote the first two problems. If it's a small piece, you might get away with it but if in doubt, practice that honourable old model making art of patience.
From a domestic point of view, polyesters biggest drawback is it stinks. You need to use it outside or away from the house. It's also very brittle. Epoxy resins have little odour which makes them far better for house projects but they rarely cure crystal clear. More often they have a brownish tint to them.