Disclaimer: this idea is so undercooked that it probably isn't even half-baked, more like lightly stir-fried.
Liquids expand when heated, but are nearly incompressible. This suggests doing a regenerated Brayton
cycle with a liquid, using a pump, hydraulic motor, and countercurrent heat exchanger (regenerator), and
the usual hot-side and cold-side heat exchangers.
This scheme has four steps like most heat engine cycles:
1. The liquid starts out at room temperature and atmospheric pressure. It enters the pump, is raised to
some high pressure P, and enters the cold port of side 1 of the regenerator. For a volume V of liquid,
work PV was required at the pump.
2. The cold pressurized liquid flows through side 1 of the regenerator, heating and expanding, then
through the hot-side heat exchanger where more heat is added to reach the final hot-side
temperature. The volume V of liquid has now expanded to V + v, and is still at pressure P.
3. The hot pressurized liquid now enters the hydraulic motor, doing work P(V+v) on it, drops its
pressure back to atmospheric, then enters the hot port of side 2 of the regenerator. Net work Pv is available
after subtracting out the work to run the pump. This could be used for traditional over-unitarian activities
such as illuminating light bulbs or pumping up that big compressed-air tank in the basement below
the demo room. ;)
4. The hot liquid flows through side 2 of the regenerator, cooling and contracting, then through the cold-side
heat exchanger, shedding heat to the environment and restoring the initial condition. Most of the heat flows
through the regenerator into the high-pressure liquid stream, leaving only a small amount to
dump to the environment.
This cycle still has the heat source and sink of a classical heat engine.
If the compression-heating effect in liquids is small, this cycle might not be Carnot-limited.
The Richard Clem engine (http://www.keelynet.com/energy/clemindex.htm)
might do something like this.