As you mentioned, it is the temperature change that causes urination.
What may work for you is this: Immediately prior to the bath, get a warm washcloth. Open his diaper, and clean his diaper area with the washcloth. Be careful with this! If it works, he may start to urinate while you are cleaning him, so you must be ready to quickly put the diaper back into place! Immediately replace the diaper.
After waiting a minute or two, transfer him to the bath. With luck, he'll be done, and won't urinate during the actual bath.
A variation on this may work for babies who tend to urinate while their diapers are being changed: open the front of the diaper, let in the cool air, wait a minute, and be ready to immediately close the diaper back up if they start to urinate. Once they're done, it should be safe to proceed.