A thermal appliance having an uneven number of closed primary circuits, each including at least two outlet points connected in series to at least one exchange zone. In each circuit, a primary fluid is circulating in an alternating cycle of period (T) having two displacement phases of a half-period (T/2) having identical flow rates and volumes but in opposite directions. The primary fluid circulation cycle is phase-shifted (by T/2N) between each of the primary circuits. The inlet of the exchange zone is connected unidirectionally to one of the outlet points of each of the primary circuits and the outlet of the exchange zone is connected unidirectionally to the other outlet points of the primary circuits so that the sum of the heat transfer fluid flow rates, entering the exchange zone, is always greater than zero. A method for optimizing the heat exchange of such a thermal appliance.