If all the seedlings are dying at the same time, the same way then the problem sounds more mechanical to me - too hot, too damp, too dry. Plants are pretty resiliant so it is rare to have every seedling die at the same time.

what kind of seeds are you planting? Could they be damping off? keeping the soil surface dry helps control that. Is there enough media in the cells? Does it dry out completely during the day?

After germination take the plants off the heat and increase the light and air circulation. Be careful to not apply water when it is not needed. Al

I don't know what kind of soil you are using, but you can try feeding the seedlings with weak (half strength) water soluable fertilizer, once they have true leaves.

Janie

If the problem is damping off, and it sounds likely, put 1 teaspoon of baking soda in a pint of water and spray the seedlings with that as soon as they start their true leaves. Once a day is more than sufficient. The baking soda is a fungicide. Always water from the bottom--it promotes root growth down rather than sideways. The suggestion of adding a light dose of fertilizer is a good one. Since the plants are on the back porch, you might consider using compost tea or manure tea (neither is smelly, but the idea of manure in the house turns some folks off. Go figure!). The teas are very mild and won't burn delicate roots. It sounds like you have a wonderful set-up that will give you more plants than you will know what to do with. You just have a minor problem that is easily fixed.