A system for winter heating and summer cooling of environments; said system substantially comprising: - a central heating and cooling equipment which includes a boiler device, or a heat pump, and a refrigerating device; said central heating and cooling equipment being suitable for guaranteeing a given difference of temperature between an incoming flow of water and an outgoing flow of water; - at least one thermal-treatment apparatus for thermal treatment of air in at least one environment; and - a hydraulic network for connection between said central heating and cooling equipment and said at least one thermal-treatment apparatus; wherein said system is configured to be connected to a radiator heating system of a traditional type, the system being characterized in that said thermal-treatment apparatus is a multipurpose thermal-treatment apparatus for winter heating and summer cooling of said at least one environment; said multipurpose thermal-treatment apparatus comprising: a compressor for a working fluid; a heat exchanger for heat exchange between the water coming from the central system and the working fluid; a temperature probe for detecting the temperature of the working fluid at outlet from said compressor; a temperature probe for detecting the temperature of the working fluid at inlet to said compressor; an external probe for detecting the temperature and relative humidity of the environment; and an electronic control unit for controlling the foregoing devices that require regulation and in that said system furhter comprises both a first heat exchanger for heat exchange between working fluid and ambient air of a convective type and a second heat exchanger for heat exchange between working fluid and ambient air of a radiant type, said working fluid being supplied at a temperature higher than dew point in any climatic condition. said system substantially comprising: - a central heating and cooling equipment which includes a boiler device, or a heat pump, and a refrigerating device; said central heating and cooling equipment being suitable for guaranteeing a given difference of temperature between an incoming flow of water and an outgoing flow of water; - at least one thermal-treatment apparatus for thermal treatment of air in at least one environment; and - a hydraulic network for connection between said central heating and cooling equipment and said at least one thermal-treatment apparatus; - a central heating and cooling equipment which includes a boiler device, or a heat pump, and a refrigerating device; said central heating and cooling equipment being suitable for guaranteeing a given difference of temperature between an incoming flow of water and an outgoing flow of water; - at least one thermal-treatment apparatus for thermal treatment of air in at least one environment; and - a hydraulic network for connection between said central heating and cooling equipment and said at least one thermal-treatment apparatus; wherein said system is configured to be connected to a radiator heating system of a traditional type, the system being characterized in that said thermal-treatment apparatus is a multipurpose thermal-treatment apparatus for winter heating and summer cooling of said at least one environment; said multipurpose thermal-treatment apparatus comprising: a compressor for a working fluid; a heat exchanger for heat exchange between the water coming from the central system and the working fluid; a temperature probe for detecting the temperature of the working fluid at outlet from said compressor; a temperature probe for detecting the temperature of the working fluid at inlet to said compressor; an external probe for detecting the temperature and relative humidity of the environment; and an electronic control unit for controlling the foregoing devices that require regulation and in that said system furhter comprises both a first heat exchanger for heat exchange between working fluid and ambient air of a convective type and a second heat exchanger for heat exchange between working fluid and ambient air of a radiant type, said working fluid being supplied at a temperature higher than dew point in any climatic condition. a compressor for a working fluid; a heat exchanger for heat exchange between the water coming from the central system and the working fluid; a temperature probe for detecting the temperature of the working fluid at outlet from said compressor; a temperature probe for detecting the temperature of the working fluid at inlet to said compressor; an external probe for detecting the temperature and relative humidity of the environment; and an electronic control unit for controlling the foregoing devices that require regulation and in that said system furhter comprises both a first heat exchanger for heat exchange between working fluid and ambient air of a convective type and a second heat exchanger for heat exchange between working fluid and ambient air of a radiant type, said working fluid being supplied at a temperature higher than dew point in any climatic condition.