So I’m not sure if this is already a thread but I have a 2005 accord 6 speed with the j30a4 and it runs perfect no codes idles perfect but when at idle if I push gas it’ll rev up then when it goes to drop down it’ll go to 500 then right back up at 750 and stay there unless I do it again. Is this normal

 

Please read the whole thread before you comment so i don't have to repeat myself.
The engine only overheats when it runs like this. It will not overheat if it decides to run normally.
Also note the engine can run normally. It's not a mechanical issue.
I know the person I bought it from isn't lying, the car didn't come with a battery and I know he couldn't afford one.. When he bought it the car was jump started and they wrapped the positive terminal with tape.