Do not be too sure that the inlet temperatures stayed the same. Many fluid delivery systems change exit temperatures when flow rate changes. However, assuming the real temperatures did not change, a few things that could explain this are:

1,  a change in radiative vs. convective heating of the TC as flow rate changes

2. striated flows, where the fluid temperature is not uniform and as you change flowrate the thermocouple senses a different part of the flow. 

3. conduction along the TC lead wires affecting the measured temperature

4. movement of the TC bead in the flow if the flow temperature is not uniform.

Also, if you are not using cold-junction-compensated thermocouple connections and the room/DAQ board temperature changed between the two measurements, you could see the same thing. In this case, it has nothing to do with the actual temperature but is associated with an inaccurate DAQ design. 

Basically, you should ascertain that the thermocouple positioning is such that it actually records the true fluid temperature. There are many sources of errors, one of them being that the stem of the sensor may conduct heat to/from the sensor to the tube exterior and thereby affect the temperature reading. The sensor position should be placed at least 10 stem diameters inside the fluid for liquids; at least 20 stem diameters for gases.

An alternative source of error is nonuniform temperature distribution in the fluid, caused by improper mixing or being in a heat exchange situation (e.g. losing/gaining signifivant heat through the tube wall). This can be remedied by using a mixing chamber at or immidiately upstream  the thermocouple location.

Conclusion: Correct temperature readings is not as simple as it sounds...

If you are performing a parametric analysis you should look into the governing equations for the double-pipe heat exchanger, meaning you should strive to non-dimensionalize the pertinent parameters. This could e.g. be the Effectiveness-NTU method described in most modern basic textbooks on heat transfer (e.g. Incropera et al, Cengel et al, Holman....) By using this method, the heat duty is nondimensionalized (effectiveness=Q/Qmax), the influencing parameters likewise (heat capacity ratio (m*cp)min/(m*cp)max and NTU=(U*A/(m*cp)min). Hence, in the end your heat exchanger performance is expressed in terms of these three variables. Your only complication is that the overall heat transfer coefficient (U) may/will vary with the fluid temperatures and flow rates. However, this can also be systemized by parametrizing individuel heat transfer coefficients of the non-dimensional form Nu=a*Re^m*Pr^0.33, where Nu, Re and Pr are the Nusselt, Reynolds and Prandtl numbers, also explained in detail in the mentioned textbooks.

(For completeness, the thermal behavior of countercurrent heat exchangers with different inlet temperatures, flow rates and fluid combinations has already been analysed/developed; the result is availale in the mentioned texts.....)