Hi Steve. Mine are already in an unheated greenhouse but I believe a poly tunnel loses heat from the sun rather faster than a glass house. I suspect that mine might be slowed a bit by the transfer but I risked it because I needed warm space for other things. If you are not really in a desperate hurry, I would wait another couple of weeks especially as inland, where you are, the day temperatures may be a degree or two higher than I get but the nights are a degree or two colder generally. I don't think they will die but it may slow them and stunt them.

Tomatoe,s need a minimum temperature of 50 deg f , below this growth is slowed down considerably, any frost and you will lose them, so if you put them in your poly tunnel, then I would invest in a heater of some sort, personally I prefer a propane heater, but you should leave the bottle outside, as any leakage, however small would kill your plants. Derekm.