A system for heating or cooling with a transfer fluid, of the underfloor type, particularly adapted for outdoor environments, comprising a plurality of basin-like bodies and contiguous basin-like bodies defining basins for containing a transfer fluid, that can be heated or cooled, said basin-like bodies (3, 3') defining a supporting structure being adapted to support a flat walkable element so that said walkable element is in direct contact with said heat transfer fluid contained in said basin, said walkable element defining a modular flooring constituted by a tile made of one or more materials selected from the group constituted by: gres, granite, marble, glass, metal, ceramics and plastics, said system for heating comprising a supporting frame adjustable in height and adapted to support said basin-like bodies (3, 3', said basin-like bodies (3,3') provided with a plurality of pins extended at right angles with respect to the lower plane of the basin, and supporting the walkable element in cooperation with the supporting action provided by said supporting structure, which walkable element skims with its own lower face the transfer fluid contained into the basin, for heating or cooling the same walkable element; each basin-like body comprising a plurality of inlets and outlets consisting of holes provided in the lateral faces of the basin-like body and each basin-like body comprising a plurality of inlets and outlets consisting of holes provided in the lateral faces and the opposite lateral faces of the basin-like body, and comprising a suction pump which can be associated to an open vessel for maintaining a negative pressure inside the basin, adapted to keep the walkable element firmly into contact with said supporting structure, and also comprising a heat exchanger in the circuit through which the transfer fluid flows, which is configured for heating or cooling the transfer fluid by bringing it to the desired temperature, wherein each basin-like body is so configured that at least one outlet faces at least one inlet of a contiguous basin-like body, so that the basin-like body and the contiguous basin-like body are mutually connected directly or with the interposition only of a sealing gasket, which is accommodated into a seat, comprised in the inlet and the outlet, and inside said sealing gasket it is possible to insert a flow throttling element, which can be constituted by a perforated diaphragm, for throttling the quantity of flow that one wishes, wherein in order to determine a desired flow of the transfer fluid within each basin, the number and the placement of the inlets and the outlets of the basin -like bodies (3, 3') to be left open is selectable, and the inlets and outlets that one wishes to close are configured to be blocked selectively by means of a flow control element, comprising a plug configured to be inserted by snap action in the inlets or in the outlets that one wishes not to be crossed by the transfer fluid, so as to define a preferential flow for the transfer fluid within the basin of the body and the contiguous body, and wherein depending on the direction of movement of the transfer fluid within a basin and between basins that belong to contiguous basin-like bodies (3, 3'), such holes are configured like inlets or outlets for the transfer fluid.