Without some data on performance, it's pure speculation as to how much power you're losing. The hotter and less dense the air is, the less power you'll get.
So for a given amount of fuel, and a given engine, you don't think higher efficiency gives you more power? Really? Increased compression ratio increases efficiency with the same amount of air and fuel. Does it increase power?I don't know about the hotter the engine the better, that's great for efficiency, but not for HP.
"In general terms, the larger the difference in temperature between the hot source and the cold sink, the larger is the potential thermal efficiency of the cycle. On Earth, the cold side of any heat engine is limited to being close to the ambient temperature of the environment, or not much lower than 300 kelvins, so most efforts to improve the thermodynamic efficiencies of various heat engines focus on increasing the temperature of the source, within material limits. The maximum theoretical efficiency of a heat engine (which no engine ever attains) is equal to the temperature difference between the hot and cold ends divided by the temperature at the hot end, all expressed as absolute temperatures (in kelvins)."