Assume the surface of the planet is experiencing ice age conditions and the facility was designed to keep the occupants alive for 6 months.

An emergency forces the permanent closure of all Heating, Ventilation, and Air Conditioning (HVAC) vents for immediate survival. Going to the surface isn't an option.

I had read, though I can't find the source at the moment, that any underground habitat requires cooling or the human's body heat will turn the place into an oven.

There seems to be some doubt that the human body will cause the temperature to rise in a closed underground chamber. If I could access this study on thermal engineering I wouldn't have asked because it would have my answer. However, the link proves that in fact, the temperature will rise if there is no venting. Natural thermal convection based on human body heat. <https://www.sciencedirect.com/science/article/abs/pii/S1359431118332563?via%3Dihub>

As for size of the facility, using the rpg's construction rules, 400 people would fit in a 240,000 square feet building.