CAN TOMATO PLANTS GO INTO THE GREENHOUSE NOW?

I have some tomato plants in 3 inch pots that have been growing indoors. Can I move them outside to the greenhouse? I am not quite ready to put them into grow bags yet.
My greenhouse is unheated.

Jazz

Thanks Elcie

Jazz

I aim for a minimum night temperature of 10C for my Toms, Cues and Peppers

They will survive lower than that, but they get checked and take quite a while to recover and get going again, and any flowers are unlikely to set (I guess no flowers yet, but probably will be in a couple of weeks?)