[Speedslug]

I would suggest sheet metal over cement tile backer board for the hot glass area.

I think shocky hot glass burn marks would be a shame on that lovely floor.

I picked up 3 foot by 13 foot sheet metal from my local heating and ventilation / air conditioning place for $18 a few years back.
The sheet metal cleans quickly and the tile backer keeps the heat away from the wood floor.