Your seedlings will grow best around 65F (18C) with gentle air circulation and lots of light. Research has proven that lowering seedlings' night-time temperature (55-60 degrees) and occasionally brushing your hands gently across the tops of the seedlings a couple minutes a day will contribute to stronger plants.
When your seedlings develop their first true leaves, they can be transplanted into larger containers. This re-potting will be good for the seedlings since this will help them develop a strong root system. When re-potting, seedlings may be set deep into their new containers to shorten the height of the seedling. The extra length under the soil will produce additional roots.
Harden Off Your Tomato Plants before Transplanting:
To reduce the risk of shock from transplanting, your seedlings should be gradually conditioned to the outdoors for about 2 weeks before planting them in the garden. Begin with 1 to 2 hours of exposure to the outside elements each day, then increase the time slowly until you can leave them out day and night.
Introducing plants slowly to outdoor conditions is called "hardening off". The longer the plants remain indoors, the harder it will be to acclimate them to the outdoors. Be sure to avoid full sun and wind when you first move your plants outside. If the temperature drops below 40F (4C), bring the plants back inside till it warms a bit.
After the transplants are "hardened off", they can be re-planted in their final outdoor growing locations, either in the garden or in large pots.