I bought my home approximately 1.5 years ago and had installed a new GE hot water heater at that time. For several months now, it keeps tripping the circuit breaker. I noticed lately that when I go to reset the circuit breaker, that particular breaker is hot to the touch, not warm but hot. Could this be an issue of bad wires, 30 some years old? And would it be difficult for me to replace the wires if so?

Hire an electrician soon! Your breaker is obviously bad, it should trip without over heating, and if its getting hot then imagine what the wires running through the wall are doing. You have a dangerous situation there and it needs to be addressed by a professionall right away.My guess is that the breaker is not only bad but is too small for the hot water unit. Please have it looked immediately.

KC could be right. What is the ampacity of the breaker box?

Even thou the breaker may now be defective, I suspect the wire connections at the breaker may have been loose, which will cause the heat.

OR, the new water heater is larger thant the original, and the circuit wiring and circuit breaker is too small.

Look at the water heater label. Look for Volts and Watts.

For example if new water heater has 5500 Watt elements and 240 Volts, then water heater draws 23 Amps. 4500 Watt elements and 240 Volts, draws 19 Amps. [Divide watts by volts to get amps]

If your water heater circuit breaker is 20 Amps, then it is too small for the job, and breaker will trip. Or if you have 12 gauge wire, this is too small for the job and breaker will trip.

4500 & 5500 Watt water heaters require 30 Amp breaker and 10 gauge wire.