Is there a rust/grease cleaning solution a radiator can soak in while building car?
Vinegar works well at cleaning radiators. It won't make it new.
Don't leave any cleaning solution in too long. It could cause damage to the radiator.
Fill it with cheap vinegar. Don't leave it more than a day. As Royce says, clean doesn't mean new. You may still end up with a clean radiator that doesn't work.
If you have grease (from say a water pump) the vinegar won't touch it. A good start solvent is needed. Nothing beats lacquer thinner for dissolving most "mystery " substance. Cheap "gun wash" from the paint supply store maybe. Another option is CLR.
I do the vinegar maybe in two stages. One day with fresh vinegar. Empty it. Rinse well. Examine inside with a bright light. If there is still "lime build up" then strain the used vinegar and use it for a second day. It is weaker,so not to agressive. Do the de-greasing first.