We investigate the phase structure of the Georgi-Glashow model at positive temperature, realized by using an asymmetric 6 3 ×3 lattice. We find a clear signal for the deconfining phase transition at all values of the Higgs coupling constant. On the other hand, there is no unambiguous signal for a transition between a "Higgs" and a "symmetric" phase at moderate [beta]; very high values of [beta] cannot be studied with the icosahedral subgroup used here, because of the freezing transition. We use some new observables as probes of the different behaviour of the system at different values of the Higgs coupling constant.