Likely not a fire hazard, but not a great situation in any case.
Honestly, overhead heating with a heat panel is effective, lasts a decade if not more and is so easy. Wood cages lend themselves nicely to overhead heating. The wood insulates well and makes for a rather efficient system when using a temperature controller.
Back to the subject of floor heating..
One way to deal with it is to make a cutout on the cage floor. Cover the whole floor with PVC foam board (aka "Sintra"
and put the heat pad under that in the cutout area. This way you heat through the plastic, not the wood. The heat pad will never touch wood.
That sure adds work and expense, but protects the cage floor rather well.
Many plastics give off toxins when heated. At 90 deg, the amount is less than say 110 deg. I believe that the material used in storage boxes is one such plastic that is not suitable for food contact if heated, yet we do it to snakes. Ceramic heaters and glass bulbs do not give off these toxins.
-----
Mark