What type will bond to raw carbon fibers?
Polycarbonate, nylon, PEEK, sometimes ABS will stick - the biggest factor is the resin choice.
PTFE, and Polypropylene will not stick for love or money
PPS, PES, PC, ABS, Ionomers (Surlyn), PSU, PBT, etc…most things will, as long as they are sized right!!! Things like PEEK/PEKK normally have no sizing, due to the high processing temps. most sizing burns off at 720f!
Whatcha doin’?
I was thinking of possible ways to make some simple parts easier… like heating up two layers of clear tp and nesting a layer of woven carbon fiber between. Speed up production basically.
Well, clear and strength to not come hand in hand. Also, TP is somewhat horrible at infusing into carbon fibers. You need a LOT of pressure (clave) to get the resin into the tows, because TP is normally not viscous. Once you start getting into strong plastics like Nylon, PPS, PEEK, etc, we are talking about 500-600+ f processing 
There are plenty of TPs (Nylon, PEEK, PPS, ect.) that can be purchased with long fiber reinforcement already in it. As Riff said the draw back is they all require very high temps (From my chats with manufacture reps 500-600F is bottom end many want 700-900F) and pressures (5-10 bar) for processing. From my knowledge of the subject (above average, below master) your plan of sandwiching dry carbon between sheets TP and heating is going to produce less than stellar results. That said if you want to put the money into trying I’d love to be proven wrong
haa. 900?!?!??! PEEK/PEKK is the highest I know of, and that is 720F
As for doing a film infusion…oh, it sucks man. You gotta match the film thickness and fabric PERFECTLY, else you have too much resin. And again, you need a clave, because plastic never goes as liquid as you want to fill the tows, unless you have hella pressure.
Although, if you just want to add CF to something, but protect it with a clear, and remain flexibleish… PP, PE, ionomers, PC, etc…clear plastics. You can get away with it, but don’t expect strength.