Any time the plant dips down into the 40's it puts it into a dormant cycle that takes up to 10 days to break. They are a equatorial plant. They like heat. Soil temperature is as important (if not more) as ambient air temperature. I try to stay around 60f if at all possible. I tend to not seed them at all until I can maintain 55+ in my greenhouse.
Make a minie cold frame for your tomatoes. Take a large cardboard box and cut the side on a diagnal. Be sure the low side is taller than your plants. If you have a light weight window screen put that over the top of the box to reduce drafts. Any way the purpose of the box is to keep the cool wind off the plants . A covering over the plants will help keep them from being burned by the bright light. Tiny plants need to be hardened off before they spend the whole day outside.
Your plants are only 2 days old couldn't you use a shop light to give them the light they need. I use 4 foot shop lights sitting on pieces of 4x4's and slide my seed flats under them . I add pieces of 2x4 to raise the lights as my tomatoes or peppers grow.
I've had mine outdoors during 45*F degree weather and they are still growing like bad weeds. I have to pot them up soon. Lower than 42*F in my experience can cause problems but I've had them come up in my garden and survive frosts and still produce as well as any I've started indoors.
Any time the plant dips down into the 40's it puts it into a dormant cycle that takes up to 10 days to break.
My tomato plants are started 100% outside in a conventional cold frame. The seedlings not only see temperatures in the 40s on many nights but also the upper 30s. The result is sturdy plants much tougher than any that I'd ever seen of those started inside.
I don't let mine get under 60 degrees. They seem to thrive best in about a constant 70 degree temp. They do get hardened off before setting in the field. Even then I try to wait until the outside temp is above 50 at night.