  The (2+1)D Georgi-Glashow model is explored at finite temperature in the
regime when the Higgs boson is not infinitely heavy. The resulting
Higgs-mediated interaction of monopoles leads to the appearance of a certain
upper bound for the parameter of the weak-coupling approximation. Namely, when
this bound is exceeded, the cumulant expansion used for the average over the
Higgs field breaks down. The finite-temperature deconfining phase transition
with the account for the same Higgs-mediated interaction of monopoles is
further analysed. It is demonstrated that in the general case, accounting for
this interaction leads to the existence of two distinct phase transitions
separated by the temperature region where W-bosons exist in both, molecular and
plasma, phases. The dependence of possible ranges of the critical temperatures
corresponding to these phase transitions on the parameters of the
Georgi-Glashow model is discussed. The difference in the RG behaviour of the
fugacity of W-bosons from the respective behaviour of this quantity in the
compact-QED limit of the model is finally pointed out.
