The reason we feel IR as warmth is partly because we are adapted to do so when it deposits heat in our tissues where we have the right nerve endings to detect it. However, we also feel other things as warmth, usually because some other event deposits heat, or because something stimulates those nerve endings, for example rubefacient liniments like wintergreen or mustard oils.
Why sunlight feels warm is partly because of its high IR content, and
partly because the IR penetrates your skin better than most of the
visible light does. Actually photon for photon, Ir contains less heat (well, less energy) than visible light does.
As for other light causing the sensation of heat, UV can do so, sort of, by damaging the skin in a way that later feels painfully hot (sunburn), though that is not quite the same thing; it is rather the inflammation reaction to the tissue damage.
However, visible light can feel warm too if it is concentrated enough. If you doubt this, focus some sunlight on your skin with a magnifying glass. Strictly speaking, as a control one should first eliminate the IR in the sunlight, but most glass lenses are not very IR-transparent anyway, and trust me, intensely focussed sunlight without IR also feels pretty hot; also, think of a laser burn.
I hope that is warmly illuminating, or at least illuminatingly warm.
Jon