Q2 begins to conduct when the voltage at the slider of the trimpot reaches about +1.3V (0.65V for D3 plus 0.65V for the base-emitter voltage of Q2. But the diode and base-emitter junction conduct at lower voltages when they get warm.
When Q2 conducts then it reduces the voltage and current at the base of Q1 so the output voltage of Q1 is sort-of regulated.
Instead of using the Mickey-Mouse voltage regulator circuit you could use an LM317 voltage regulator IC set to exactly 1.44V. A series resistor could limit the max current and the trickle-charge current will be very low when the battery cell's voltage reaches 1.44V.