I have a family room addition over a slab that is currently heated by a
boiler unit. The register is perhaps 4-5 feet in length. Normally,
its 6-10 degrees cooler in that room than the other rooms.

Here are a couple of variables to throw in.

I am adding a bedroom to the west of this room, thus this room will no
longer be exterior on three sides, just two. A large and very leaky
picture window unit is being replaced with a wall and a door leading to
the new, well insulated bedroom. Four small (but older) window units
will remain in the family room.

Will the fact that this room will be much better insulated from the
west due to the new addition warm it up? My HVAC guy says its a colder
room b/c the boiler register sits on an interior wall now.

I could get my electrician to wire an additional heater in this room
for probably 300 bucks if he is here anyway running wire in the new
addition.

On this cool morning (30F outside) it is 72 in the kitchen, and 66 in
the family room. Maybe this is not a huge difference but it feels cool
to me.

Should I have him throw another unit up to warm up the room or will it
warm up becoming an interior room?

Thanks