My heated propagator looks like a tropical garden

Sounds too humid to me.
I would let some air at them.
I only leave the lids on for germination, off they come after that.

It's still very early though - have you got somewhere to put the plants when they've germinated?

Depends on a few things, is your propagator thermostically controlled?, is it in a greenhouse which is likely to get quite hot anyway when the sun comes out?

I've got it down to a fine art in the last few years, and if the propagator isn't thermostically controlled you will need to keep an eye on daytime temps and turn on and off, also open greenhouse door on hot days. There ought to be vents on top of the propogator which I would recommend to leave open, you could also do with a through flow of air (my hubby rigged up a fan (from a car) in the ceiling and a long tube of plastic down to the floor to recirculate the air).

 Other tips, dont over water, only water when drying out, not automatically everyday, and cover seeds with vermiculite not soil, stops damping off and other fungal diseases.

You get away with them in the living room?   How??    Just looking for advice here, really, I would get just so many sarky comments ... You must be good at sweet talk!   

My plastic bags don't have vents either.

"I've got an unheated greenhouse, but I've got a plastic mini greenhouse inside at the end for extra heat."

I reckon you need a minimum of 10C (at night) for Toms otherwise they "Stall" - and take ages to get going again. Mind you, nothing to stop you bringing the pots into the house at night if it looks like being too cold in the greenhouse - they don't need light at night, of course!

The tomatoes are up !

Currently in the study now with a big tin foil surround !