Though if this is a peat fire the water in the peat may have partially evacuated during the freezing process - I'm not so certain that the volume needing to be sent from ice -> water -> vapor would take more energy than the larger volume sent from water -> vapor... I really have no knowledge of ratios here but there are at least some processes working against increasing the amount of energy that needs to be expended to heat the surrounds.
Additionally, if this fire is mostly underground then it's likely that you've got some oven action going on where a lot of the heat produced by the fire isn't just whisked away by air to dissipate to nothingness - instead it's trapped by the insulation of earth and being converted into phase changes more efficiently.
Additionally, if this fire is mostly underground then it's likely that you've got some oven action going on where a lot of the heat produced by the fire isn't just whisked away by air to dissipate to nothingness - instead it's trapped by the insulation of earth and being converted into phase changes more efficiently.