Cleaning water jackets 225

Long story but here is the condensed version. The car had the original engine when found in a barn. The owner got the engine to run but he said it kept overheating. He switched the engine out for a 1969 engine. I buy the car and want it to be as original as possible so when I purchased the car I had the original 1965 engine rebuilt. Once installed I noticed the engine would run hot by the gauge. It would pin all the way to the right. Then it will back off but never in normal range. I have ordered a auxiliary temp gauge and temp gun but if I need to clean water jackets while the engine is in the car what is the best way to do such. Has anyone got any ideas?

Thanks for reading