We present detailed studies of the dependence of the low-temperature properties of HoNi2B2C on the annealing temperature. We could shift the superconducting transition temperature Tc reversibly and continuously by changing the thermodynamic state of a sample via thermal treatment. The magnitude of this shift is as large as about 10% of Tc. The superconducting transition temperature is correlated with the occurrence and strength of re-entrant behaviour. Upper critical field measurements of two samples annealed at 800°C and 1100°C indicate that the magnetic ordering temperatures are not affected by the thermal treatment. A reversible shift of Tc with annealing temperature has also been observed for YNi2B2C and LuNi2B2C with non-magnetic rare earth ions.