Problem with seedling transplanting

The issue (if there is one) is whether the draft from the windowsill is too much at night when the temperature drops. On the windowsill, I tend to put a cover over my seedlings at night and leave them exposed during the day.

I also grown them in an unheated greenhouse, but when the temperature is forecast to fall well below 10C at night its time for them to come inside. So it then comes down to how many seedlings you've got and how much space you've got.

A couple of years ago I grew 1000+ tomato seedlings. I grew them in plugs (54 plants to a tray) and moved them in and out of my garage every night and morning. I grew then to 3 inches tall in the plugs by which time the greenhouse wasn't going (much) below 10C overnight and they survived and did well

I plant the baby plants into deep transparent plastic cups, with just two inches of coir/vermiculite/compost mix in the bottom. The sides of the cup keep the draughts off a bit.

I add more compost mix as they grow, and the extra roots the plants grow from the stems seems to benefit them in the long run. They do need some weak feed though as there is not much nutrition in the compost mix.

It seems worth the little bit of extra effort imho

I didn't think the seedlings needed to be in the propagator so long, surely once they come through the soil they can go somewhere that is light and at normal room temperature?