I have a related question. I was flying my Piper Archer 181 at 11,000ft and was levelled off, in clear air above clouds, with full RPM and sufficient leaninig. When I applied the carb heat, the engine began to run roughly. I left the carb heat on, thinking there might be a bit of icing. Once the carb heat was turned off, the engine was fine. Applying the carb heat again straightaway, the engine ran rough again. At the time the engine was near the end of its 2000 hour lifecycle and later was shown to have lost about 10% of its power over it's life. I was also pretty much near the service ceiling.
Was the roughness, due to the thinner air, possibly compounded by by the heat applied from the exhaust manifold? I wasnt overly concerned. We had to get a new engine later on anyhow, but havent since been up that high, so I dont know if my experience was 'normal' for the type of plane / height.