Honeybees do not hibernate: they cluster and shiver their flight muscles to generate heat, burning honey as fuel. The colder it gets, the more honey the cluster must burn to hold its core above the survival threshold — and that capacity is limited by how many bees are shivering and how well the hive retains the heat they make.
R = insulation / 10
demand (kg honey/day) = max(0, (28 - T_out) * 0.018 / R)
capacity (kg honey/day) = colony_size * 0.0000045
burn = min(demand, capacity)
stores -= burn * dt_days
if capacity < demand: core temperature drifts down (deficit)
if stores = 0: core temperature collapses toward T_out
cluster dies when core temperature < 10 C
- Outside temperature — the colder it is, the bigger the gap the cluster must close by burning honey.
- Hive insulation — thicker walls (50-120mm) raise thermal resistance R and cut the honey needed for the same outside cold.
- Colony size — more bees means more shivering muscle and a higher maximum heat-generation capacity, but also more mouths drawing on the same stores.
- Honey stores — the fuel reserve; run out before spring and the cluster has nothing left to burn.
Below roughly -35 C even a strong, well-provisioned colony can lose the thermal race, and once the core drops under about 10 C the cluster can no longer hold together — bees chill individually and the colony is lost. That is why almost all of a beekeeper's real winter-prep work happens in late summer and autumn, long before the cold sets in.