Firminy, a town in south-east France, has been shrinking for decades, its steel-built glory days long gone. But perched on a hill sits its pride: l'Unité d'Habitation, Le Corbusier's final project - a concrete monolith where two-thirds of the apartments are social housing, and the whole thing is a listed historic monument since 1993.

Designed for a 1960s climate, not the four heatwaves France has already endured this summer, the tower now feels like an unlivable furnace. Inside, temperatures regularly hit 35C, spiking to 40C. Residents are resorting to sleeping on floors and balconies, or hanging tinfoil and blankets over windows because shutters are banned - any facade change requires approval from the architectes des bâtiments de France (ABF).

"I slept on the floor because it was the only place I could stay cool," says Aurélie Mohamed, a five-year resident. Nathalie Rouchouse, who moved in 15 years ago, slept on her balcony. Chantal Hospital, who's been there 26 years, is trying to move out: "I never want to live in a historic monument again."

While private owners of listed properties get 40% renovation grants and tax breaks, social renters are stuck with the worst of both worlds: underfunded HLM maintenance and strict heritage rules. Habitat et Métropole, the social landlord, didn't answer questions. And to add insult to injury, about 20,000 tourists a year pay to visit the site, but none of that money goes back into the building - it only covers guides, advertising, and insurance. Residents live in a museum where they're the exhibits, sweating behind DIY blankets.

In July, the French government proposed giving local councils more power to modify historic buildings, making ABF advice merely advisory. Conservative critics at Le Figaro decry a "concrete and soulless France," but residents already live in a concrete block - one without shutters.

The Fondation Le Corbusier only this year started discussing heatwave impacts on its sites, planning to dig through old plans for shutter-friendly designs. But with French bureaucracy, this could drag on until the homes are uninhabitable. Heatwaves in France are expected to increase fivefold by 2050, and while the rich caused the climate crisis, social housing residents - without AC or shutters - will suffer first.

"At some point, a choice will need to be made," says Hospital. "Does the building stay residential, as Corbusier intended, or does it become a museum?" Right now, it's both - and neither works.