Tomatoes need two things to grow successfully inside during winter.
Indoor tomatoes require 12-16 hours of light a day. Even plants in a sunny window or in a greenhouse may need a few extra hours under grow lights during winter’s short days. Heat
Indoor tomatoes grow best when the air temperature is between 65º-85ºF. If your house thermostat is set lower, your house is drafty, or your greenhouse isn’t heated, keep plants warm with a space heater or seedling heat mat.
What kinds of tomato plants should you grow indoors?
Cherry or plum tomato indeterminate varieties perform best indoors.
Why indeterminates? It can be tempting to choose compact tomato varieties to grow indoors because their size is, well, compact. But most compacts are determinate tomatoes, which produce a finite amount of fruit within a short time of about 2-3 weeks and then stop. Indeterminate varieties, on the other hand, continue to grow throughout the winter and will produce fruit in abundance. Never fear - you can choose indeterminate varieties that may not be labeled "compact" but won't create a jungle in your family room.
Why cherry or plum varieties? Small fruited plants (cherry or plum tomatoes) produce a large number of fruit and ripen quickly.