It is so important to be patient during the hardening off process. I've tried to rush it in the past and you can really screw up your plants if you don't let them ease into the outdoor weather properly.
I always try to put plants out too early and regret it. I would just wait until there is no worry of cold nights. Actual sunlight is great but cold temps slow down plant growth. I would think the combination of T8s and warm inside temperature at night would be better for your plants than...
I now start my pepper seeds in 3.5 inch square pots so I don't have to pot up from tiny cells. With these larger pots, I don't think my heat mats change the temperature very much at the top of the soil where the seeds are.
You could dig up a seed and take a look at it...if the germination process started and the seedling broke through the seed itself but then dried out I would think it isn't good anymore. If you have enough seeds you might want to plant some more to be safe.
You might not have any super hot peppers ready by the beginning of August (I never do), but there are a lot of generous people here who could hook you up with whatever you need...I'd say plan your pepper eating contest!