Brother-in-law “stealing” our cat with his super warm room—Am I overreacting?

My husband and I have a cat, and his younger brother recently moved in with us after college. He barely engages with us or the animals—always shuts his door and keeps to himself. The issue is that he always has his heater cranked up, making his room super warm, and lately, he’s been leaving his door open at night, hoping our cat will go sleep with him.

He has never fed her, never done any of the care or work for her—just occasionally picks her up. Meanwhile, we’re the ones feeding, cleaning, and taking care of her. I feel like he’s luring her in with the heat, and it’s making me so mad. Yes, I get it, the cat decides where she wants to go, but I feel like it’s not a fair choice when she’s drawn to the warmth.

No, we can’t make our room warmer to compete; it’s already at an optimal temperature for us. I get headaches if it gets hotter.

How do we handle this? Am I overreacting, or is there a way to set boundaries without being unreasonable? Any advice is welcome!