I've never had putty heat up while drying but I have had fibreglass resin (epoxy) char mixing cups (I don't use resin as a filler on a model anyway). However I have had problems with the chemicals in the putty warping or melting the styrene if the part is very thin (vacuform) or the putty has been applied very thickly in a single coat.
Either is very easy to prevent. First apply several thin coats of putty, allowing each coat to dry throughly before adding the next and in the case of very thin plastic (such as vacuform parts) I try to use something that doesn't effect the plastic. Currently I use Durham's Wood Putty in those places I don't or won't use putty.
As far as what type of putty to purchase, there are literally dozens of choices out there. My personal preferences are the single part automotive putties. Although the modeling putties (Squadron, Tamiya, Gunge etc) work very well I've stuck with the automotive types for at least 3 reasons. 1- They can be found in every automotive parts store and in most hardware stores. (I live in a small town of maybe 3000 people and I've got 3 different places here I can buy what I need), 2. They come in acrylic and laquer base and in various textures. 3. They're a lot cheaper than the modeling variety. I use Dupont's "Spot n Glaze" Red laquer based putty. I bought a 2 lb tube for 12 bucks a little over 5 years ago and am getting ready to buy a new one. I'd have to spend a heck of a lot of bucks to get the same amount of modeling putty and what I've got works very well for me. I would reccommend you bite the bullet, buy several types and give each a try to find what works best for you.