A couple of options I have seen:

Buy a piece of Flexwatt or THG and secure it to the inside of the bottom with aluminum tape. Then cover the entire floor of the enclosure with a piece of linoleum. Secure the linoleum to the floor and seal the edges with silicone.

Or, if you have access to a router, buy a single piece of ceramic floor tile from Lowe's or Home Depot. Cut the tile, if necessary, to your desired size. Cut an opening in the bottom of the enclosure so that an inch or so of tile overlaps the hole on all four side. Use the router to cut a recess the thickness of the ceramic tile just wide enough so the tile drops in flush with the floor. Drop the tile onto the remaining lip and secure with silicone. Also use silicone to seal any minor gaps on the edge. Your heat mat or Flexwatt/THG will then attach to the bottom of the tile with aluminum tape.

Good luck on the build!