What others said. I’ve been on a guided Catacombs tour, and I’ve been a tour guide and amateur explorer of the caves near my home town Maastricht.
Both those caves and the catacombes are technically not (natural)caves; they are man-made limestone mines. In maastricht, those mine corridors are empty. In Paris, 18’th century Parisians filled the corridors with stacked bones from the clean up of the overflowing cemetaries in Paris.
Limestone, a building material, is a remnant of prehistoric seas. Lime stone is found in horizontal layers, not that deep below the surface. Usually no deeper then 100 feet below the surface.
So the temperature in such a cave will be the general underground temperature: a constant 10 degrees Celcius, all year round. It will feel chilly and damp in summer, and chilly and warmish in winter. It will always feel damp, but you won’t see water dripping from limestone; the material is porous and acts like a groundwater sponge.
To feel warmth underground, you have to go much deeper. It starts to get hot around 6000 feet deep.