This is also a good point to clarify. A higher wattage card will surely contribute to higher ambient temperatures. However, like you said, a dedicated mining rig can be put in another room.
As someone that mines on my main productivity/gaming rig when I'm not using it, I'm more concerned about package temperatures and heat soaking into other components. For example, a lot of modern motherboards have M.2 slots for solid state storage lined up behind where a dual slot graphics card might go. A cooler letting heat stick on the GPU or pushing it toward the SSD might affect the longevity of the SSD, but a cooler pushing heat out the back of the case or elsewhere in the case but away from the motherboard might be better for your other components. In this way, a cooler that disperses more heat into the room can be better for the components adjacent to the GPU.