Warning, long and rambling
I'll take what Chris wrote a step further, though I probably should not have. Synthetic winch line is just standard run of the mill high-tech, single braid sailboat line, which in some cases is just repurposed from fishing boats. Fisheries Supply, Annapolis Performance Sailing and Layline, just to name a few, all have several types of line that will work well, usually about $1.50/ft - $1.80/ft depending on size. Amsteel Blue is good (which is very different from Amsteel -- probably not ideal for this application), Lightning Rope, Ultrex, D12, Technora, AS-78 (aka Dynex Dux 75), etc., all could work well. Stay away from PBO as it is allergic to UV. I would also stay away from Vectran unless it is blended with spectra/Dyneema because, while it is more UV stable and stronger than Dyneema, it does not handle chafe well.
I think the heat issue may be a bit over stated. If you are concerned, have a sleeve made to cover the first wrap of the drum with
MGP Nomex Cover Only as it will absorb more heat than a cordura sleeve (which is absolute king for chafe protection). If you are really paranoid, figure out how much wire you need for one wrap of the drum and have that length of wire spliced into a synthetic rope so you have wire for the first 20' and synthetic for the next 80'.
Also, as Chris pointed out, each line has its strengths and achilles heels and you need to know as much about the different options and how to work around specific compromises before you buy. For example, Dyneema (Amsteel et. al.) degrade under high heat and exposure to UV light, but the line is slippery allowing it to handle chafe well -- remember chafe means both external (on a rock) and internal (line fibers against line fibers). Aramid (Kevlar, Technora, to some degree Vectran) is pretty strong and impervious to everything but cannot handle any chafe well (external as well as internal) and it does not degrade slowly, it just blows up (edit -- also not stable in the presence of solvents, so be careful about spilling engine fluids on it). This is why a lot of new lines are a blend of fibers, like Dyneema and Vectran -- Vectran can handle the high loads while the Dyneema reduces internal chafe thereby significantly raising breaking loads and allowing a smaller diameter line.
Lots of options, and while synthetic line is relatively new to the off-road world, it is old hat in the marine industry and a lot of the problems have already been thought through. You just have to ask the right questions to the right people, I'm just suggesting that perhaps in this one instance, your local 4x4 shop is not the right people to ask.