Where to keep tomato seedlings

I've got some tomato seedlings which are just germinating now :happy:. I've been keeping them on a windowsill in the house but when I've done this before, they've gone a bit spindly, presumably because there's not enough light? I've got an unheated greenhouse so I've been putting them out there in the day when it's been warm & then bringing them in again at night. The problem is when I'm at work - the greenhouse is getting too hot already but if I leave the door open it's too cold by the time I come home . It has automatic roof vents but even so the temperature has been really high already  Any suggestions?

Thanks for your help. I'll do that now. Am glad there's hope for my seedlings!