Temperature aside, most seedlings will do well if using soil less mix, sterile water (I use RO filtered), and adequate ventilation. With the exception of a good soaking immediately after planting, the soil should never be waterlogged. IMO you also want to let the soil dry out almost to the point of wilting before watering again; if the soil surface never dries out, it will promote the rapid spread of algae at best, fungi at worst... which leads to damping off.
When I first began starting my own plants, I fell for those "mini greenhouse" trays with the transparent covers. The results were, well, educational (in other words, a failure). Germination was initially good; but mold quickly overran the entire tray, and killed all of the tomato seedlings before they had their second leaf. I had a similar issue crop up when I first used the setup I have now, because the trays against the wall had poor air circulation... so when the plants were 4-5" tall, mold began to appear on the stems & I lost a few. When I put the remaining plants outside, they recovered. I use a fan at low speed now to prevent stagnant air, and have lost nothing since.