My first thoughts were along the lines of flaps like Brian said in post #2. I'm not familiar with heater box design on P38's but if flaps move sideways and have become free to swing (actuator broke or something) it would be easy to imagine turning causing them to swing sideways.
I have known heaters get hotter/colder when turning, going uphill/downhill or with changing engine rpm due to water flow aspects but usually when there's a problem with water flow or just not enough water in the system.
It runs on LPG so will have an LPG pressure reducer plumbed into the heater system. I've known cases where reducers have been plumbed in parallel and most water has gone through the reducer at the expense of flow through the matrix in some conditions but centrifugal force during turning can change the dynamics and pushed more hot water through the matrix. Or plumbed in series and overall flow has been restricted but centrifugal force has caused more overall water flow perhaps by seeing the reducer (if fitted at a high point) is more fully bled up.
Although the problem is described as occurring when the heater is being used, if AC is on it could be due to something that causes the AC clutch to disengage when turning right.
Cornering might imply body roll and/or a change in engine rpm.