Equal and opposite fix heat commands shouldn’t cause energy drift, and I think it can also be made to work with SHAKE with reasonable energy conservation, but I haven’t tested this. Peter, you could try it with SHAKE turned off and a smaller timestep.
Peter, also I’d recommend trying the same simulation with both of your fix heat commands turned off to make ensure you get really good energy conservation. In the past, other users have seen that poor energy conservation can get really bad with fix heat turned on.
Poor energy conservation can be caused by a variety of things, but you might check SHAKE tolerance and kspace solver tolerance. Also check timestep size and force field discontinuities, and make sure you’ve got a well equilibrated initial configuration.
I imagine it is possible that your flipping experiment simply masked the energy drift caused by such underlying issues in your simulation.
Paul