A heat transfer system, comprising: a building; a first two-phase heat transfer fluid vapor/compression circulation loop disposed outside of the building, comprising a compressor, a heat exchanger condenser, an expansion device, and the heat absorption side of a heat exchanger evaporator/condenser, connected by conduit in a closed fluid circulation loop and having disposed therein a first heat transfer fluid having a critical temperature of greater than or equal to 31.2°C; and a second fluid circulation loop disposed at least partially inside the building that transfers heat to the first two-phase heat transfer fluid vapor/compression circulation loop through the heat exchanger evaporator/condenser, comprising the heat rejection side of the heat exchanger evaporator/condenser, a liquid pump, and a heat exchanger evaporator, connected by conduit in a closed fluid circulation loop and having disposed therein a second heat transfer fluid having an ASHRAE Class A toxicity rating and an ASHRAE Class 1 or 2L flammability rating; wherein the second fluid circulation loop includes liquid second heat transfer fluid flowing, when the second fluid circulation loop is operated, in the conduit between the heat rejection side of the heat exchanger evaporator/condenser and the liquid pump and flowing in the conduit between the liquid pump and the heat exchanger evaporator at a higher pressure than a liquid pump inlet pressure, and gaseous second heat transfer fluid flowing, when the second fluid circulation loop is operated, in the conduit between the heat exchanger evaporator and the heat absorption side of the heat exchanger evaporator/condenser, wherein the heat exchanger evaporator transfers heat to air blown by a fan through another conduit. wherein the first heat transfer fluid comprises propane and the second heat transfer fluid comprises sub-critical fluid CO 2. wherein the second heat transfer fluid further comprises nanoparticles having a specific heat and a thermal conductivity that is greater than either or both of the specific heat and thermal conductivity of the second heat transfer fluid without the nanoparticles; wherein at least a portion of the conduit of the second fluid circulation loop between the heat rejection side of the heat exchanger evaporator/condenser and the liquid pump and at least a portion of the conduit of the second fluid circulation loop between the heat exchanger evaporator and the heat absorption side of the heat exchanger evaporator/condenser are outdoors. a building; a first two-phase heat transfer fluid vapor/compression circulation loop disposed outside of the building, comprising a compressor, a heat exchanger condenser, an expansion device, and the heat absorption side of a heat exchanger evaporator/condenser, connected by conduit in a closed fluid circulation loop and having disposed therein a first heat transfer fluid having a critical temperature of greater than or equal to 31.2°C; and a second fluid circulation loop disposed at least partially inside the building that transfers heat to the first two-phase heat transfer fluid vapor/compression circulation loop through the heat exchanger evaporator/condenser, comprising the heat rejection side of the heat exchanger evaporator/condenser, a liquid pump, and a heat exchanger evaporator, connected by conduit in a closed fluid circulation loop and having disposed therein a second heat transfer fluid having an ASHRAE Class A toxicity rating and an ASHRAE Class 1 or 2L flammability rating; wherein the second fluid circulation loop includes liquid second heat transfer fluid flowing, when the second fluid circulation loop is operated, in the conduit between the heat rejection side of the heat exchanger evaporator/condenser and the liquid pump and flowing in the conduit between the liquid pump and the heat exchanger evaporator at a higher pressure than a liquid pump inlet pressure, and gaseous second heat transfer fluid flowing, when the second fluid circulation loop is operated, in the conduit between the heat exchanger evaporator and the heat absorption side of the heat exchanger evaporator/condenser, wherein the heat exchanger evaporator transfers heat to air blown by a fan through another conduit. wherein the first heat transfer fluid comprises propane and the second heat transfer fluid comprises sub-critical fluid CO 2. wherein the second heat transfer fluid further comprises nanoparticles having a specific heat and a thermal conductivity that is greater than either or both of the specific heat and thermal conductivity of the second heat transfer fluid without the nanoparticles; wherein at least a portion of the conduit of the second fluid circulation loop between the heat rejection side of the heat exchanger evaporator/condenser and the liquid pump and at least a portion of the conduit of the second fluid circulation loop between the heat exchanger evaporator and the heat absorption side of the heat exchanger evaporator/condenser are outdoors.