Yes, you can grow heirloom tomatoes indoors! Start seeds 6-8 weeks before the last frost date. Use a sunny window or grow lights. Once the seedlings develop true leaves, transplant them into 5 gallon containers for support.
Add a tomato cage as well. Maintain even moisture, temperatures above 60°F, and provide supplemental lighting for 12-16 hours daily. Prune the plants for air circulation. Move the plants outdoors after the danger of frost has passed.