Tomato seedlings once they have grown their second leaves can be moved into direct sunlight. Make sure the weather is not above 80 degrees Fahrenheit and it is not too windy. Move seedlings that have been grown in shade gradually into bright light, for a few hours in the morning and move them back into part shade in the afternoon. Hardening off seedlings is the gradual process of moving them into sunlight and getting them used to the full sun. This process can be done gradually to avoid any leaf burn.