That's too quick a thought: If the barrel does not move sideways, you still CAN have uneven distribution if the fuel is biased left or right. The air will distribute evenly, but liquid has different inertia and might not distribute evenly at the T-junction.

Basically, a change in "relative tune" throughout the throttle range. On my twin, the both cylinders would show a different progression in temperature throughout the throttle range. For example, at idle the left hand cylinder would basically cool down due excessive rich mixture, at mid throttle both would run "about equal, and at full throttle the right hand cylinder would run the coolest because the rich condition changed from one cylinder to the other throughout the throttle range...

A barrel NOT moving sideways, does NOT automatically mean both cylinders will run equal, but at the very least I would expect the difference to remain more or less constant.

One thing that is very important, is that both temp probes are located as precisely the same as you can get them, because measurements vary with location. Get that right first, otherwise you are only chasing your tail.