The answer to 'why is my backflow preventer no hot water' is that the backflow preventer itself is not the cause of the lack of hot water. A backflow preventer is a plumbing device that prevents water from flowing back into the public water supply, and it has no direct impact on the hot water system. The lack of hot water is likely due to an issue with your water heater or the plumbing that supplies hot water to your fixtures.
Some common causes of no hot water with a backflow preventer include a malfunctioning water heater, a problem with the thermostat or heating element, a leak in the hot water pipes, or a blockage in the hot water line. If you're experiencing no hot water, it's best to first check your water heater and the hot water plumbing system to identify the root cause.