We had something like this when the ignition switch would not return fully to the "Run" position after starting the engine. The car would run but some electrical things would not such as the horn, radio, etc. I can't recall how the heater was affected.

Next time this happens try gently turning the ignition key a little bit counterclockwise and see if things start working. If they do, the electrical portion of the ignition switch needs replacing, not too big a job.