In this paper, gravothermal oscillations are investigated in two-component clusters with a range of different stellar mass ratios and total component mass ratios. The critical number of stars at which gravothermal oscillations first appeared is found using a gas code. The nature of the oscillations is investigated and it is shown that the oscillations can be understood by focusing on the behaviour of the heavier component because of mass segregation. It is argued that, during each oscillation, the recollapse of the cluster begins at larger radii while the core is still expanding. This recollapse can halt and reverse a gravothermally driven expansion. This material outside the core contracts because it is losing energy both to the cool expanding core and to the material at larger radii. The core-collapse times for each model are also found and discussed. For an appropriately chosen case, direct N-body runs were carried out, in order to check the results obtained from the gas model, including evidence of the gravothermal nature of the oscillations and the temperature inversion that drives the expansion.