I have hot lug nuts

I recently had a flat after about an hour of driving. When I changed the right front tire the lug nuts were so hot they burned my fingers. Why? There was/is no vibration, pull or brake-on light from that wheel. I’ve never experienced hot lug nuts while changing a tire. Car is a '98 Ford Taurus with 120,000 miles.

Time for a complete brake inspection…Your R/F is obviously dragging and we don’t know if the L/F was also hot…A stuck caliper, a defective flex-line, using your brake pedal for a foot rest, it can be any of these things…Driving in traffic can warm the brakes up too…That’s how brakes work…But when the lug-nuts get so hot they will burn you, there is usually a problem…

At the very least, you need to replace the calipers on the brake for that wheel.
Even if the brake is not binding sufficiently to cause a “pull”, it is binding sufficiently to overheat the brakes on that wheel.

An overheated brake mechanism may also mean that you need to replace the rotor, and–of course–you want to see just how badly-worn the brake pads are. Also, make sure that you flush the brake system and refill it with new brake fluid of the correct specification.

After doing all of the above-noted work, if the symptoms persist, then you may need to replace the flexible brake lines. Brake lines can deteriorate on their inner surfaces after many years, and since your car is now at least 14 years old, the flexible brake lines may well be in need of replacement.

The only thing about your post that find confusing is the reference to a “brake-on light from that wheel”.
I have never seen a brake warning light specifically for one wheel.

A bad wheel bearing will also transfer heat to other parts. To find out whether the problem is a wheel bearing or brakes jack the corner of the car up and wiggle the wheel. If there’s play in the hub area you have a bad bearing.

Thank you all for the suggested repairs. I’ll try them.

It’s a front tire, so be careful when interpreting the wiggle - the wheel is going to wiggle a bit anyway since it’s a steer wheel - don’t let that fool you into thinking you have a bad bearing.

If the brakes on that wheel are not dragging, etc. then what about the possibility of an underinflated tire causing this seeing as how an underinflated tire can overheat?

I was just wondering if this is the case how many miles the car had been rolling like that and the reason why the tire went flat. (Sidewall problem, etc)

Were you driving in the mountains, or really hurrying? It would have been good to feel the other lug nuts to see if they were just as hot. One wheel hotter than the others indicates a real problem but it isn’t necessarily in that wheel. It could be a frozen caliper on the other wheel that isn’t letting the brake apply. In that case this wheel would be doing most of the stopping.

Jack up the front wheels with the car in neutral and the parking brake on and see if they both spin free.