heating methane in a vacuum chamber
The problem is where the energy for heating comes from not the gas or the mechanism of heating

Rocket engines often use burning fuels to produce thrust because chemicals are a very good store of energy and burning often produces hot gaseous products.

Yes, you can produce hot gases by other means (there are electrically driven plasma rockets and you could, maybe, heat gases with microwaves or similar radiation). But the problem you have is where to get the energy for that process? A self-contained rocket has to have an energy source and that source has to be compact and a slight as possible (a long electrical cord to an electric socket isn't practical in orbit or in space). Just about the best way to store energy is various combinations of reactive chemicals (eg oxygen and kerosine) and the easiest way to turn that into thrust is burning. The only other approach know to work well is to put a nuclear reactor on the rocket as an energy source but that has obvious disadvantages for other reasons.

Rocket scientists have spent a lot of heroic effort to optimise mixtures of (often dangerous) chemicals to achieve better thrust. For a good summary read John D Clark's Ignition where he traces the history of trying to make use of extreme oxidising agents like chlorine trifluoride to get better performance.