More heat improves thermal efficiency, that's why thermostats have gone from 160 back in the old days to 195 in modern high efficiency engines.
Here's the problem: the engine's components absorb heat and pass it to the cooling system. The absorbed heat is wasted because it is not used to expand the gas in the cylinder, it is used to add heat to the engine's components. In a ceramic (or adiabatic) engine, this heat is not lost because the components don't absorb it. In a metal engine, the kinetic energy (the stuff that actually moves the piston) is created with the heat left over after the materials are completely heat soaked. So the cooler you run the cooling system, the more heat gets diverted to heating the engine components. This is what led Detroit engineers to 195 degree thermostats some years ago.
On the other side of the problem, you have the specter of detonation from too much heat. Our universal gas law says the fuel/air mixture will gain heat as it is compressed, and at some point, it will auto-ignite from the increased temperature. So we have to keep the combustion chamber cool enough to prevent this from happening. There are a few ways we can do this.
The fuel itself has a heat of vaporization, so the type of fuel will help remove heat from the compression process. Alcohol fuels like methanol and ethanol are excellent for this because they require significantly more heat than gasoline to vaporize. Methanol and nitromethane are wonderful for engines running a total of about 30 seconds with only 4 seconds at full output. These fuels just don't really need much additional cooling in a drag racer.
Running an air/fuel mixture on the rich side of stoichiometric also helps because the excess fuel also absorbs heat and reduces the tendency to auto-ignite. This is one of the prime reasons why tuners start rich and go lean in the search for power. Rich is relatively safe, and leaner becomes increasingly dangerous.
We can also run the cooling system at a lower average temperature to help reduce combustion chamber temperatures, but as we already noted, this will lose thermal efficiency. The ideal cooling system would maintain a fully heat soaked combustion chamber without promoting detonation from auto-ignition. Given the current state of automotive cooling system design, there is a lot of opportunity for improvement, but the cost of those improvements isn't very economical.
I have toyed with the idea of a reverse flow cooling system with independently computer controlled valves for each cylinder to allow a closed-loop control for combustion chamber temperature. The concept is to maintain full heat soak while monitoring for knock and adjusting coolant flow to keep the engine on the verge of knock without actually causing detonation. Unfortunately the sensor array and the controls to do this are prohibitively expensive, and the efficiency gains over the present design do not warrant this kind of investment in a mass produced machine. Even a one-off would be absurdly expensive and the payoff would be tiny.
Ceramics are the great hope. Cummins has had engines since the 80's that run at or above 98% thermal efficiency, but they just don't do it for very long. The other thing conspiring to squash this technology is the oil companies would cringe with fear if we suddenly improved the thermal efficiency of the entire fleet by a factor of three. Sales would drop precipitously, and there would be no need for lubricating oil in these ceramic engines, so a whole product line would go away. Not very enticing to an oil-based economy.
So, that's the theory. Yes, a hotter thermostat raises combustion efficiency. It brings problems with it, and brings the user a little closer to the edge of disaster. All the information about the parts expanding beyond service limits fails to realize these parts were all designed to run at a given temperature and as long as the engineer and machinist know what that is, the pieces can be designed to work just fine.
