The faster leather dries the more it'll shrink and harden, so you apply heat -- no, only warmth -- to dry it faster. If you overdry it and steam all the moisture out of it you'll ruin it.
When you get a piece of leather wet all the way through and start drying it out you reach a stage when it looks and feels dry but it's still soft and pliable. (That's the way most leatherwork is done, by the way.) It's when it dries further from that stage ... if it dries slowly it'll still be almost as soft and pliable when it's fully dry and won't shrink much. If you dry it faster by putting it next to a light bulb or in an oven at low heat it'll shrink and harden. You've probably seen hard leather puukko sheaths, formed to the knife -- that's how it's done. If you go too far ... I once saw a fool pick up a red-hot piece of steel wearing leather weldor's gloves -- the leather smoked and turned black and shrank onto his hand so he couldn't get it off. We had to cut it off him and it wasn't easy to cut and his hand was badly burned, though he recovered. The leather was almost as stiff as wood, and about as easy to cut.... Once leather gets that way soaking it doesn't soften it up again.
So, my advice is to dampen it, wait till it's dry to the touch but still soft, then warm it a little and see what happens. Keep checking on it so you don't overdry it. If it doesn't shrink and harden enough, dampen it again and repeat the process with a little more heat. If you're cautious it could take several tries before you get it right, but that's better than not being cautious enough and ruining your leather (especially if your hand is inside it at the time...).
There's probably some local leatherworker who could do it for you, but there's no reason you can't do it yourself and be successful without previous experience if you're cautious and don't mind making several tries before you get it right.
I can't tell you what temperature to use ... it depends on the individual piece of leather and the humidity and how hard you want it. Without experience you just have to go by trial and error.
-Cougar Allen :{)