The main issue is protecting your footings from frost, but that might not matter here either. Is your cottage built on rock? I know that bedrock is never far from the surface in Parry Sound, and if your foundation walls sit on rock, there’s really nothing to worry about. Frost won’t affect the foundation. Even if your place is built on soil, there’s a good chance that the basement won’t drop below freezing, even without any additional heat. The basement in my own home has been completely unheated for the last 20 years and temperatures have never dropped below freezing even when it’s -30ºC outside.
What we really don’t know is the temperature of your basement during winter with so supplemental heat. If it were to drop below freezing in the basement, there’s a slim chance that the soil under the footings could expand and crack the foundation. Is there a year-round neighbour you could trust to check on basement temperatures periodically, turning on the heat if things get near freezing at floor level? One winter’s monitoring would give you the information you to proceed with confidence.