Ordinary 12 volt halogen bulbs (GX5.3) are either 'Dichroic' or not. It is the former that allow heat out of the back by having a reflector that does not reflect infra-red, only the visible light. Some downlight manufacturers in their instructions say these should not be used in their fittings, but dichroic bulbs are the more readily available and one should assume that they will end up in fittings regardless of the makers' instructions.
On the other hand some design their fittings and firehoods to work satisfactorily with dichroic lamps. See for example
www.illuma.co.ukI assume that there is a two-foot gap between ceiling and roof as the other dimensions are given in feet. Provided there is ventilation of this area so that the heat build-up is minimised, I would not be too worried about the heat heading towards the roof.
Neither would I be concerned about heating of the false wood ceiling. The radiated heat is mostly upward and to a limited extent downwards and does not actually fall on the wood. Most of the heat going in the direction of the wood will be the heat conducted from the fitting to where it passes through and is clamped to the ceiling. There will be some convected heat as well, but the ventilation mentioned above should deal with that.
I cannot recall how polycarbonate burns exactly, but I think it needs a reasonable heat source with flame for ignition, then it's a bit like wood but will drip burning droplets - these might be capable of igniting wood. Subject to high temperature it will become soft and sag and eventually fail, hence its use for skylights to give venting.
Hope this helps.