Wiring a reliable temperature switched outlet
Unless you go to more expensive industrial products, you'll have trouble finding thermostats that operate reliably at near freezing temperatures.  Using a space heater to heat up the entire crawl space is going to be inefficient when all you need is to keep the pipes above freezing.
Heat tape seems like a much better option, it's made for this exact purpose.  There are lots of options available if you shop around.  Many work without a thermostat, the heating element automatically stays at a temperature just warm enough to keep the pipes from freezing.  The heat is applied exactly where it is needed.  You run it inside pipe insulation so very little of the heat is wasted heating the crawl space.