Dynamic response of temperature change when identical fluids flowing mix together

As shown in the below figure , there is a mixing of a fuel in a system. the mass flow rates m1,m2 are different, the pipe diameters are all equal but are different in length.I need to get the temperature time response at the outlet after the mixing at length of 'a' .

1) Is the temperature response linear or does it exponential ? 2) How would i apply the Newton law of cooling when the fluids are flowing ?