The concrete slab that the oven floor is placed on is a monster heat sink. Without any insulation underneath, it is radiating heat into that area like an oven - only you can't get to it. If one wall had been partially built you could have used it for short term wood storage, as in the photo below.
Without any insulation on top of the dome and the dome being enclosed in a brick house you are radiating heat into the "attic".
As Pink Floydd says - Break down the wall.
You definitely need to insulate the dome. If there is zero insulation on top of the dome and your oven enclosure is similar to this
then you can open up part of the roof or get in through a hole cut in the upper wall and "blow' in perlite. As for insulating under the floor you need to create an access hole that is structurally sound. What is needed underneath is insulation board (Cal-Sil) probably 3 to 4 inches thick bonded to the underside of the floor.