The invention provides a heat pump system and method comprising a Shape-Memory Alloy (SMA) or Negative Thermal Expansion (NTE) core (2a, 2b) positioned in a housing and adapted to absorb heat and store energy in response to a first fluid inputted at a first temperature. The housing is configured to receive a second fluid via an inlet wherein a device changes pressure in the housing to cause the SMA or NTE core to change state to release the heat absorbed into the second fluid. An outlet is adapted to output the second fluid at a higher temperature than the first temperature.