I have a warm 10-3 wire leading to my drier. There is a 30 amp breaker for it. The wire is approx. 48 ft long. The breaker is hot to the touch when in use. Is this a problem?

"The wire is approx. 48 ft long." do you mean the cable run from breaker to dryer is 48' ?

Could be a defective circuit breaker, or loose wire connections, or loose connection where the breaker plugs into the panel.

In any case, have the breaker and panel checked.