Is it ok to wash a car with temporary plates?

No, it's a Class E Felony, and you could go to Federal PMITA prison.

Seriously, what kind of question is that? Of course you can wash your car. Just don't get the paper plates went. If you do get them wet, they could be ruined and you'd have to buy more insurance.

For future reference, any time you have a question about the legality of a situation, consult a local attorney.