The growth of cadmium mercury telluride (CMT) by molecular beam epitaxy requires control of the substrate temperature within a narrow window of a few degrees for growth of twin-free layers on the (111)B and (211)B orientations. It is shown that a thermocouple in contact with the substrate holder does not necessarily provide a sufficient temperature stability and reproducibility. Improving the thermal contact between the substrate holder and the thermocouple by wetting the interface between them with gallium results in a drastic improvement of the substrate temperature control. Reproducible twin-free growth of CMT on (211)B, as well as on misoriented (III)B CdZnTe surfaces have been demonstrated without any change of set points for the substrate or cell temperatures during the growth run. This demonstrates that the growth of twin-free layers does not require a change in the growth conditions with time.