A non-surgical and non-therapeutic method of estimating a temperature T p of blood at an inlet of a blood treatment device for a pumped fluid system with a storage vessel, the method being implemented automatically by a controller operable with the blood treatment device, the controller being connected to a pump and a temperature sensor, the method comprising: using the controller, pumping blood in a blood circuit from the inlet through the blood circuit to the temperature sensor positioned along said blood circuit and remote from said inlet such that heat is transferred between the blood and an external environment of the blood circuit as the blood flows from the inlet to the temperature sensor; said pumping including, automatically, using the controller: pumping blood at a first flow rate F 1 and then subsequently pumping blood at a second flow rate F 2; recording temperatures T c1 and T c2, respectively, for each of said flow rates, indicated by said temperature sensor; calculating a temperature T p from temperatures T c1 and T c2 and flows F 1 and F 2 independently of a measured temperature of said external environment, said calculating including an initial calculation where temperature T p is calculated from temperatures T c1 and T c2 and flows F 1 and F 2 or T p is set to a predefined value, initially which may be only an estimate such as a normal body temperature for humans, and the value of T p is set without relying on any data directly indicative of the temperature of the external environment of the blood circuit; and outputting data responsive to the calculated temperature T p. using the controller, pumping blood in a blood circuit from the inlet through the blood circuit to the temperature sensor positioned along said blood circuit and remote from said inlet such that heat is transferred between the blood and an external environment of the blood circuit as the blood flows from the inlet to the temperature sensor; said pumping including, automatically, using the controller: pumping blood at a first flow rate F 1 and then subsequently pumping blood at a second flow rate F 2; recording temperatures T c1 and T c2, respectively, for each of said flow rates, indicated by said temperature sensor; calculating a temperature T p from temperatures T c1 and T c2 and flows F 1 and F 2 independently of a measured temperature of said external environment, said calculating including an initial calculation where temperature T p is calculated from temperatures T c1 and T c2 and flows F 1 and F 2 or T p is set to a predefined value, initially which may be only an estimate such as a normal body temperature for humans, and the value of T p is set without relying on any data directly indicative of the temperature of the external environment of the blood circuit; and outputting data responsive to the calculated temperature T p. pumping blood at a first flow rate F 1 and then subsequently pumping blood at a second flow rate F 2; recording temperatures T c1 and T c2, respectively, for each of said flow rates, indicated by said temperature sensor; calculating a temperature T p from temperatures T c1 and T c2 and flows F 1 and F 2 independently of a measured temperature of said external environment, said calculating including an initial calculation where temperature T p is calculated from temperatures T c1 and T c2 and flows F 1 and F 2 or T p is set to a predefined value, initially which may be only an estimate such as a normal body temperature for humans, and the value of T p is set without relying on any data directly indicative of the temperature of the external environment of the blood circuit; and outputting data responsive to the calculated temperature T p.