So.. my day time bulb just burnt out, and the only light bulbs I have are standard general electric LEDs, and it gets really hot, can the LED handle 60w/ 120v? Here's the box
If you're talking about leopard geckos and you also have a heat mat under the enclosure, you don't really need lights at all. My understanding also is that LED's don't give off heat in particular. The light in the picture looks like an incandescent. If you're depending on that light to provide the only heat, I imagine it will be OK. If you already have a heat mat you really don't need another heat source above.
That's not an LED, it a regular incandescent bulb, what we call a black light. It's not recommended because it provides a bit of light. You don't want light at night, just heat.