I just checked the DA40 flight supplement which we had for the 1.7 Thielert, and the situation is even more complicated.
With diesel, or a blend of diesel and Jet-A (anything over 10% diesel would be considered a blend) the minimum engine starting temperature of the fuel is indeed -5C, but the minimum take-off temperature is +5C. So once you've got the engine started, you've got to wait for the fuel in the main tank to reach +5C. Furthermore, fuel transfer from aux to main is not guaranteed if the fuel in the aux tank is lower than +5C.
In contrast, the limit on Jet-A is -30C, both for starting and take-off.
The fuel is heated because the excess fuel in the common rail is led back to the main tank, via a coil in the aux tank. And the fuel is heated up in the common rail not just because of the ambient temperature in the engine compartment, but also because of the pressurization to ~400 bar.