I'm cold and in desperate need!! Please help!!!!

I have a 3600 watt 240v window air conditioner in the house that uses a nema 6-15 plug and receptacle. I'm pretty sure that it is wired into two 20 amp breakers. I am looking to buy a 240v garage heater to use inside my house to supplement the 120v electric heaters that I already have. I can't plug in any more of the 120v heaters without tripping the breakers. I found a garage heater that has a three way switch that does 3000/4000/5000 watts. The data sheet on the 3000 watt switch says it draws 12.5 amps. Could I wire up this heater to run at least on 3000w (low) and draw the 12.5 amps without any problems? Also should I use 10/3 wire to connect it? Link to the heater. Thanks for any help! https://www.manualslib.com/manual/2031837/Ken-Brown-Kbh-5000w.html?page=4#manual

https://www.amazon.com/KEN-BROWN-Controls-Workshop-Warehouse/dp/B08K41HH5B/ref=sr_1_5?crid=MMVDU27VT2NX&dib=eyJ2IjoiMSJ9.nNuGdD5W8BHSxQkDIY3N04I8q2ZCEzpwYkPTphcmEZEwYjx1XL900XA19znS0ZpKFPPB2gBqsc3VcBM7BG2AwNJvGZR8vZhSUULospH9i0HfTg-VBSJPZ-IAyPq7D8rl5zZFg8L7LTnT8Am1A5x_qvKBz-f62GZtNk2EpE-prFqlOnRoVYmFyxo9FrZO_JkV1lxAEr4vNbji_WpiJf8cSrzdYySrE7WWUnP1E_8uhk2BT3ltA8jSv-xpezoWIhwjKIXd3ghs6Y63cxCH_PTX6NBYhUyNnF2kRxPxO7W8S0T4zLeXUqFQHvJjwGDw6UEtDIOiEfyatGcHXRVVNJA-b_uEoJicKtgqsIXd2FXXDRD-oDkxHpHWjs4SJX1EjEZzSybyUI53iiEKoYQD1V-VPRAIFUMRpO0uX_9fOzFnxo4U42NcqxDJ8bjyoVLr6-gv.4fNM5UaCBvh3c1zNHI7OkmS5bTPe6RG1dlYt4L--RC4&dib_tag=se&keywords=3000%2Bwatt%2Bgarage%2Bheater&qid=1737423257&sprefix=3000%2Bwatt%2BgRAGE%2B%2Caps%2C126&sr=8-5&th=1