Heating system for a floor of a cabin of an industrial vehicle, wherein the cabin is provided with an internal air heating system where at least one air-fluid heath exchanger receives from at least one supply conduit a heating fluid from the cooling system of the engine and has at least one return conduct to a return side of the engine cooling system, wherein the heating system comprises: a control valve interposed along said return conduct and movable between at least - a first position where fluid flows along said return conduct directly to said return side and - a second position where at least part of the fluid flowing thought the control valve is diverted to an input (13-a) of a serpentine having an output (13-b) for discharging fluid towards the engine cooling system; said serpentine being placed over a floor of the cabin; a cabin floor mat placed above said serpentine and containing a plurality of energy-storing elements made in a material that changes its aggregation state from solid to liquid by receiving heating energy from the serpentine thus storing thermal energy; said stored thermal energy in the material is given back towards the exterior of the floor mat when the material changes its aggregation state from liquid to solid; temperature sensor means configured to detect the temperature T mat of the cabin floor mat; control means designed to drive said control valve; said control means being designed to set said control valve in said second position when said detected temperature T mat falls below a first limit T low so that a first energy storing phase is realized; during said first energy-storing phase the thermal energy of the fluid flowing in the serpentine is transferred to said energy-storing elements changing their aggregation state from solid to liquid; said control means being designed to set said control valve is in said first position when said detected temperature T mat overcomes a second upper limit T high so that a second energy delivery phase is realized; during the second energy-delivery phase the thermal energy previously stored in the energy-storing elements is supplied to the exterior of the mat when the energy-storing elements change their aggregation state from liquid to solid. a control valve interposed along said return conduct and movable between at least - a first position where fluid flows along said return conduct directly to said return side and - a second position where at least part of the fluid flowing thought the control valve is diverted to an input (13-a) of a serpentine having an output (13-b) for discharging fluid towards the engine cooling system; said serpentine being placed over a floor of the cabin; - a second position where at least part of the fluid flowing thought the control valve is diverted to an input (13-a) of a serpentine having an output (13-b) for discharging fluid towards the engine cooling system; said serpentine being placed over a floor of the cabin; a cabin floor mat placed above said serpentine and containing a plurality of energy-storing elements made in a material that changes its aggregation state from solid to liquid by receiving heating energy from the serpentine thus storing thermal energy; said stored thermal energy in the material is given back towards the exterior of the floor mat when the material changes its aggregation state from liquid to solid; temperature sensor means configured to detect the temperature T mat of the cabin floor mat; control means designed to drive said control valve; said control means being designed to set said control valve in said second position when said detected temperature T mat falls below a first limit T low so that a first energy storing phase is realized; during said first energy-storing phase the thermal energy of the fluid flowing in the serpentine is transferred to said energy-storing elements changing their aggregation state from solid to liquid; said control means being designed to set said control valve is in said first position when said detected temperature T mat overcomes a second upper limit T high so that a second energy delivery phase is realized; during the second energy-delivery phase the thermal energy previously stored in the energy-storing elements is supplied to the exterior of the mat when the energy-storing elements change their aggregation state from liquid to solid.