I was searching for something different but saw this post is at the top of results for chicks having abnormally hot feet. There can be several causes to it. There is a strain of mycoplasma that specifically targets the feet /legs , and can cause them to feel hot and feverish there. I’ve seen it spread somewhat easily in indoor birds, perhaps due to flooring/carpeting.
Another common cause, especially in chicks can be coccidiosis, they often can exhibit fever and contrary to popular belief bloody droppings are not always present. Often it can be easily missed; foamy/bubbly droppings and frequently stinky diarrhea-looking droppings can be a sign. Feeding medicated feed is not a guarantee against birds contracting it.
Some microscopic parasites can cause tender and feverish or itchy feet too. Bird parasites are not easy to spot like dog and cat ones. Most are microscopic and can’t be seen with the naked eye.
One such example is feather lice variants. Your birds can get them from wood shavings at the feed store you got them from; you won’t easily see them for several reasons.
some feed on the feather shafts, some feed on the keratin in the scales of the feet, or near the beak or face (called scaly face or scaly leg mites in such cases) and some are blood-feeding parasites as well.
Nearly all of them will cause itching and irritation and can cause feverish symptoms at the source as well