is it not the case that you need to harden the plants off for a bit - so stick them outside for a few hours each day and let them get used to the cold before throwing them in at the deep end?
I've got chillis and Toms on the go and during the day i take them out of the heated propagator so the temp drops form 30 degrees down to 18 degrees, but they go back in at night
but i'll soon be leaving them out of the propagator 24/7 then in another 3/4 weeks i'll move them out to the greenhouse
I've got shallots and early tatties in containers in the greenhouse, i now take them outside in the morning and leave them out during the day and pop them back at night - they'll be getting left out all night soon (i need room for the chillis and toms!!! LOL)