Thermostatically controlled loads (TCLs) are an attractive source of responsive demand. This paper aims to provides a better understanding of the relation between thermal properties of TCLs and their suitability to provide energy arbitrage and frequency services. An approximate analysis on the basis of dimensionless parameters is used to visualise the relative abilities of eight classes of TCLs. The results are compared to those obtained from a formal optimisation approach, in the context of a GB case study. Additional studies are performed to investigate the impact of increasingly flexible frequency services and physical variations of TCL thermal models (thermal conductance and temperature deadband).