A fluid circulation pump (10) with synchronous motor (14), equipped with fluid heating device (40), particularly for washing machines or the like, of the type comprising a rotor (18), equipped with a permanent magnet being rotation-driven by the electromagnetic field generated by a stator (15) equipped with pole shoes (20) with the corresponding windings. This pump (10) has also a magnetic flux sensor (22) of the rotor (18) and a control unit (24) a signal from the magnetic flux sensor (22) at least a typical parameter of said fluid and a comparator this parameter with a reference value and to cut the power supply of the fluid heating device (40) off upon reaching a threshold of the predetermined reference parameter.