As to your original problem, you should just install fiberglass
batt insulation between the floor joists. That would go a ways
towards eliminating any coldness from the floor. BUT, the floor
is most likely not the problem as it is rare that a floor will
allow a room to become too cold. Most heat loss is from the
walls, ceiling, and especially windows. I will bet that this
alcove has windows on three sides, doesn't it?

--
Robert Allison
Rimshot, Inc.
Georgetown, TX