Tóth and Bobok [1, 2] developed an attractive model for the temperature of deep coaxial borehole heat exchangers with a constant flow rate. The model is based on Ramey’s approximate solution for the thermal interaction of a well with the surrounding rocks . Their temperature solution for the fluid in the annulus and the inner tube involves four coefficients that are given by four boundary conditions. It appears that a numerical method is required to obtain these four coefficients. This article provides a new temperature solution for the same model, which is complete. It demands only two boundary conditions – the first is the given injection temperature, and the second is that the temperature is the same in the annulus as in the inner tube at the base of the well. The new solution is extended to a multi-segment solution, where each segment may have different properties, such as casing, the width of the annulus, radius of the inner tubing, material properties, rock properties and the geothermal gradient. The multi-segment model is demonstrated with a deep coaxial borehole heat exchanger with three different parts. The temperature difference between the outlet and the inlet is studied regarding two dimensionless numbers. It is found that the maximum temperature difference occurs when the dimensionless heat transfer coefficient for the casing-rock is much larger than one. A second necessary condition is that the dimensionless heat transfer coefficient for the insulator between the inner tube and the annulus must be much less than one. The power leakage from the inner tubing to the annulus is also at a maximum at these conditions.