Generally speaking seeds need 65 - 75 f to germinate, once germinated keep around 45-50 f and moist.
Depending on how you are germinating really, ie. propagator or as you say, leaving on the window sill.
I would cover or place the sowing pots in clear plastic and give them light, not direct though, if you do not have a heated propagator.
Once germination has taken place, remove from the plastic or propagator.
Works for me.

Sorry Dian, have just re read your question. You have already germinated the seeds, by the sound of it.
I try to keep my "hot" greenhouse around 50 f.

Many thanks for your quick reply Littlelegs.