OK I'm genuinely curious now.. wouldn't the fact that a computation has taken place mean that energy has been used to do work (non-heat)? My intuition tells me that it would not be possible to simultaneously use energy 100% to generate heat and do something else at the same time. For example if you used an electric motor to move a weight against massive friction, it could be that 99% of energy is lost to heat due to resistance in wires and friction, but if the weight moved, it would mean that not all energy was lost to heat.