Electron spin resonance (ESR) thermochronometry can in principle be used for reconstructing thermal histories of the upper ~ 2 km of the Earth's crust. We have analysed the ESR ages of Al and Ti centres in quartz from Fergusons Hill-1 borehole in the Otway Basin, Australia, to assess their trap parameters under natural conditions. The apparent ESR ages of both centres decrease with increasing temperature (42.9–56.2 °C). A feasible sequential quadratic programming optimisation algorithm was applied to determine the optimal trap parameters based on the assumption of first order kinetics and thermally static condition. The estimated activation energy and frequency factor of the Al centre in quartz were 1.5 eV and 1.11011 s−1, respectively. This was in excellent agreement with a re-analysis of samples from the Eldzhurtinskiy granite, a highly dynamic geologic system, for which we obtained 1.5 eV and 1.01011 s−1. The trap parameters of the Ti centre could not be obtained from first order kinetics for the Fergusons Hill samples, but the samples from the Eldzhurtinskiy yielded 1.6 eV and 2.41011 s−1. Further studies on trap kinetics under better controlled laboratory conditions are required for ESR thermochronometry.