I think you are in a good situation, relatively speaking. Seedlings
actually prefer cooler temperatures (in the 60s) once they have
germinated. Start them on top of your fridge, where it is warm, then
move them outdoors. Find a way to moderate temperature swings inside
the enclosure. You can have it under ground, you can add water
containers (I have a 55 gallons drum), and you can have ventilation.
Sterilize your trays well because the conditions will be generally
conducive to damping off.