So I took uncooked, frozen chicken burgers and put them in the oven at about 350 and left them for about 15 minutes. But then I had to leave my apartment so I took them out. They were warm and unfrozen. I put them in the fridge and so I want to know - can I cook them tomorrow morning for lunch?
They are probably safe to eat, although it's difficult to tell for sure.
The basic rule is that food should spend no longer than 2 hours in the danger zone between 4 and 60 Celsius. Assuming that it took them less than 2 hours to go from "warm and unfrozen" to fridge temperature (which is below 4 Celsius), they are officially safe to eat. With small food items like burgers, this shouldn't be a problem. It is large pots of food such as soup which may take too long to cool down from just-cooked to fridge temperature, but a hamburger has much less volume.