So does it feel like the heater is stuck on? On most cars the "heater core" -- a small radiator -- is in the passenger footwell where there's more room for it.. However, if the temperature control is on the warm side -- or the KNOB is on the cool side but the actual valve in the heater core didn't respond properly -- you could definitely get that warm feeling all over, even with the fan off.
Does it seem hotter, and windier, down there with the vent control to "flow through" than it does on "recirculate"?
Try putting the A/C on and see if it blows warm or cold (assuming you have A/C -- and it works!)
Or does it feel as though the floor itself is what's hot? Perhaps the exhaust system components down there are heating it up -- maybe normally (i.e., your car has always been like this but you never noticed because you always had shoes on); maybe because a heat shield has gone missing; maybe, as someone else noted, because the catalytic converter is hotter than usual.
--Joe