The only flaw in your plan is you asume that most heaters are 120v but most are 240v with a 3 speed electric fan motor sorry but you need o go back to the drawing board also most home hvac units draw way more amps than what you think i know because im an electrician and i also use to be a hvac man. ...

You need to not only search tesla but search "tesla coil". The coil uses transformers to step up 120 volts up to over 1 million voltes but very benine to the human body he was able to light up even burned out florecent light bulb over 50 foot away with no wires.