Infrared is the peak of the frequency range emitted by objects that are roughly body temperature—that doesn’t mean it’s the only frequency that makes objects warm.

In fact all light that isn’t perfectly transmitted or reflected makes things warmer.

That’s false. You can literally not only feel heat from, but you can in fact set things on fire with, a completely monochromatic green laser with a wavelength exactly in the middle of the visible spectrum. No infrared, no ultraviolet. Lots of heat transfer. You could do it with an ultraviolet laser too if you were careful enough and could get around ultraviolet’s tendency to destroy molecular bonds completely before they even have a chance to burn chemically. It’s not just lasers either, any light source is going to deposit energy in the form of heat on anything that light touches. Any light contains a large amount of energy and some of it will get absorbed by anything it interacts with, and that’s still true whether it’s infrared, ultraviolet, somewhere in between, or all the above.

Infrared has a special relationship with heat, yes, because of the distribution of blackbody radiation, but “No” is absolutely the wrong answer here. The right answer is “Yes, but… it’s complicated”.

This is correct but also glass blocks both ends of the spectrum. Really just visible light goes through glass. You get some near IR passthrough but not much.