I recently read about "Steam jet cooling" on wikipedia -- a type of air conditioning that was used on railroads, back when trains were steam driven.
In the original system, waste steam from the pistons was passed through a steam injector, which sucked water vapor out of a water-filled evaporator.
water in that evaporator boiled then boiled at a very low pressure, and absorbed heat from the train's passenger compartment, providing cooling.
The output of the steam injector (the original steam sent in, plus the steam sucked from the evaporator) was then sent on to the condensor.
A second steam injector was then used to move liquid water from the condensor back into the boiler.
It seems to me that the same setup, (boiler, evaporator, condensor, and two injectors) minus the mechanical power generating parts of the steam engine, could be used to create a heat-powered heat pump.
It would be a vapor compression heat pump, but with no moving parts.
Assuming that it works, it could be used in the same kinds of applications as an absorbtion chiller or absorbtion heat pump.
The advantage this idea has over a conventional vapor compression heat pump should be obvious:
1) There are no moving parts, so it should last indefinitly, and be fairly quite.
2) It consumes heat (solar heat perhaps, or else combustion of oil, gas, wood, etc.), not electricity as a power source. Thus, it wouldn't contribute to brownouts or blackouts, nor would it be much effected by a brownout.
3) Any refrigerant can be used, even water. Water is as nontoxic as you can get, and has a fairly high COP, but conventional (electromechanical) vapor compression heat pumps using water need a large or fast (and thus expensive) compressor. A steam injector might possibly be a cheaper type of compressor.
In comparison with absorbtion heat pumps / absorbtion chillers... item number 3 above is probably the only real advantage... but, considering that many absorbtion heat pumps use ammonia as the refrigerant, this is still an important benefit.