I have done the insulation and vapor barrier and dehumidification of my crawl space. It is still cold. Can I put a propane space heater in there to keep it warm?

I would not recommend it. You have exhaust fumes to think about and you would have to make sure there was proper ventilation. And by design crawl spaces and basements are suppose to be cold zones. Just be careful. Depending on how big the area is you may be able to use your existing furnace for an option, it would depend on the type of heat you have (i.e. forced hot air, etc.)

Trademark is correct, do not both trying to heat a crawl. If the vapor barrier is in place along with insulation just let it be. You walls are insulated with a vapor barrier and you don't try to heat the outside with a heater. If your crawl has louvers you should close them for winter, that's about it.