Thats not a radiator issue, you probably have a breached headgasket that is allowing boilover when engine is cool and sealing up when warm, it may sound odd, but it does happen.
You need to contact a well versed mechanic like @syncview to test the system properly.
Cleaning radiator in place is possible, its done with citric acid solution. It also cleans out the entire engine, pipes and heater in dashboard too, but if you see brown sludge in cooling system already and are seeing boilover, you may completely kill the system after cleaning. (An non-maintained cooling system is very expensive to restore)