In theory we can break down the sense of sight into subcomponents, too. It's only the visual cortex that processes those raw inputs into a coherent single perception. We have two eyes but generally only perceive one image, even if the stereoscopic vision gives us a good estimate of distance, and one eye being closed or obscured or blinded fails pretty gracefully into still perceiving a single image.

We have better low light sensitivity in our color-blind rods but only have color perception from our cones, and only in the center of our visual field, but we don't actually perceive the loss of color in those situations.

So yeah, someone putting a warm hand on my back might technically set off different nerve sensors for both temperature and touch, but we generally perceive it as a unified "touch" perception.

Similarly, manipulating vision and sound might very well throw off one's proprioception, because it's all integrated in how it's perceived.