While I cannot give you chapter and verse (you could contact Cal DMV for it) my wifes cousin drove a school bus for about thirty years and her boss more than that. They are very aware of the regs in Cal and five minutes is max for them. I assume it applies elsewere in the state.
I know that our fleet services constantly put out notices about letting or gas rigs idle until the heater would heat or until the temp guage moved. Their rule was cold start, no reving the engine and thirty seconds of idle then put it gear and idle out of the yard.
Most of our rigs required a Class B commercial license.