Since a ramjet isn't constrained by turbine inlet temperature like a gas turbine is, it seems to me that it should be able to achieve a higher thermal efficiency, given that it's operating at a speed that results in a comparable compression ratio. Is this true?
The Carnot condition notwithstanding, whether a ramjet actually operates at a higher "hot end" temperature than a turbojet is questionable, as well as whether a comparable percentage of thermal energy in the exhaust stream is converted to kinetic energy.
Further, just because there's no turbine, doesn't mean there's nothing in the hot part of the engine that can melt -- combustion chamber walls are made of real material, as is the flameholder, and due to cost of exotic metals, likely aren't as heat resistant as first stage turbine blades. Even a very simple, low-powered ramjet (see YouTube) can operate at a temperature that makes the hot section glow from heat; one capable of propelling a high speed aircraft will presumably run even hotter, requiring tradeoffs in efficiency to prevent thermal damage.