Hello Robert and welcome to Permies!
how do you regulate temperature?
Mostly by the addition of wood/fuel to the RMH, you also have some control if you throttle/open the feed tube
Carcinogens?
You might get an occasional smoke back when starting or stopping the rocket mass heater. To avoid this I have been using a propane torch to preheat the J-tube, by the time I add the wood the entire system is already drafting. If you do not properly seal the ducting then you may have a leak. Cob will form a nice air tight seal over the ducting before leaving the house. In my case I have not completely sealed all the joints in the ducting and will have a leak or two. I will eventually seal them with masonry.
Once the heater riser is really hot it will burn most of the smoke/carcinogens (search Youtube user: broaudio, flue gas analysis of rocket mass heater)
Girlfriend - aesthetics?
This is entirely dependent on your girlfriend's tastes. I don't think I am even remotely skilled enough

to assume what your girlfriend's taste preferences would be.