The air warmed vaporizers I use are the Century or Zenith. I'm not familiar with an air warmed Cobra. With the correct vaporizer, the warm air from the cooling fan that keeps the engine cool warms the vaporizer nicely- it's warm to the touch.
I've seen some systems where they use a Zenith air warmed high pressure regulator, then the fuel goes to a standard Model J or Cobra (w/ no coolant flow or warm air keeping it warm), then to the mixer. Those systems work very well also.
Freezing up can mean it is allowing too much fuel to exit, and running poor would confirm this. If the new regulator is running ok I suspect it would be fine to be cool to the touch. I once saw a small AC engine with an Impco regulator that had antifreeze installed in a closed loop hooked into both coolant ports and it did great.