Yes, that’s the answer.
But is shouldn’t be that hard to do. Especially because it’s in an interior recess, behind the radiator – it’s not very visible, so you don’t have to have a ‘perfect’ patch on the interior wall.
To do this:
- Temporarily remove the radiator,
- Tear out the interior plaster & lath wall. Discard.
- Insert a piece of 2" pink foam insulation into that hole, up against the brick exterior. If you can shove this up further behind more of the wall, that will help.*
- Use the Reflectix you mentioned to sheath the foam, to provide more reflection of the heat.
- Place a sheet of drywall to cover the hole in the interior wall. Mud & tape the edges, sand & redo until it’s reasonably smooth.
- Paint the wall to match the rest of the room.
- Put the radiator back into place & reconnect.
Should be possible to do this yourself in a long weekend, if you’re reasonably handy. Or hire a pro – should be only half a day or so for them.
- Polyisocyanurate (ISO) foam would work also. It is about 1/3 to 1/2 more insulation, but also is more expensive. Might not matter for such as small space. But also might not make that difference if the whole rest of the wall is uninsulated.