Bottom heat helps to speed the germination process. Garden centers and catalogs sell heating cables made just for this purpose, but you may also set the pots or flats on top of your water heater to take advantage of its warmth for germination.As soon as the seedlings emerge, they should be moved to an area with full light, such as a sunny window or under grow lights. They should have light on them for about 12 hours a day and should be kept at a temperature of 70-80 degrees.
Fertilize the seedlings with a water-soluble fertilizer when they're about 3-4 weeks old, but dilute the fertilizer to about half the strength recommended on the label. The little tomato plants will be accustomed to fairly steady and warm temperatures indoors, and planting them directly outside could come as quite a shock to them, especially when nighttime temperatures are still cool.
About a week before it's time to plant them in the garden, begin to gradually introduce them to outdoor conditions. This is called hardening off, and it simply involves moving the plants gradually to conditions more like what they'll experience in the garden.Start hardening them off by moving the plants to an enclosed porch for a day or two, then to a sunny spot outdoors that is protected from the wind. If the temperature threatens to take a drastic downward dip, bring the plants back indoors until it warms up outside again.Tomatoes were originally found only in very warm climates. They don't like to be cold and should not be planted outside until the danger of frost has passed and the soil has warmed up. That's typically late May or even early June in northeast Ohio.