Yes but by a weird coincidence most of that heat can be provided by heat pumps at a similar 3-5x ratio.

(it's not a coincidence, it's the exact opposite formula. You can only get 20% out of a certain heat engine because running it in reverse would be a 500% efficient heat pump, and the closed loop can't be more than 100%. This still applies even if the engine isn't built to be able to act as a heat pump, because some other engine could.)