Germinating in the conservatory?

Hi everyone,

I spent a couple of hours sowing seeds into trays and cells yesterday and have put them in the conservatory. However, I've been thinking, will it be warm enough for them to germinate? I don't know the exact temperature out there, it's nice and warm during the day but quite chilly at night. 

Would I be best off moving them to somewhere warmer until they germinate and then move them into the conservatory, or shall I just leave them there?

In case you're wondering I have sowed the following:

Courgettes, pumpkins, butternut squash, tomatoes, kohlrabi, sweet corn, sunflowers and zinnias. The courgettes and zinnias are in propagates whereas the others are in the open.

I've attached a couple of photos. Also, the radiator is not on and will not be turned on at all.