For eggs to hatch they need to be incubated in the range of 99 F. But development can take place below that temperature. The embryo in a fertile egg is alive and developing. If it ever totally stops developing it dies. How fast it develops depends on temperature. Below 80 F development is not going to be fast enough for you to ever notice. The warmer they get though the faster they develop. It's not that they will hatch, but they develop to a point they can't sustain it and die.
I think refrigerating them in your case is probably a good idea. They would still be safe to eat, but there is a YUK! Factor that many people, including me, might have problems with.