Thanks for the replies. I still have the issue.
I drained the system today and removed the drain valve. I sucked the remaining water out with a wetvac and looked inside with a flashlight and my snake camera. The flash light worked well enough. I saw a small pile (1/4 cup) of white sediment in the back left section of the water heater and I used the wetvac to suck it up. The bottom of the tank looks good. No rust, etc. I opened the cold water inlet and filled the tank back up with water, opened all hot water faucets until all the air blew out and had a stready stream of water. I then shut the faucets off, opened the gas valve, light the pilot, set the temp to 130 degrees and now the burner is on heating the water.
Let me restate the problem. I could have nice hot water for the shower one morning and the next morning it is luke warm.
@speedball1: That is my complaint. I'm trying to figure out what/where the problem is.
@massplumber2008: I understand the process of cold water entering the bottom of the tank and the hottest water rising to the top and out to the faucets. Help me understand the working of the water heater. The bottom of my water heater is very clean. I have a gas water heater (State Select model PR650XODSV2) with one burner on the bottom. The thermostat seems to be about 4 inches above and to the left of the drain valve. If the thermostat is set to 130 degrees, where physically in the tank is the water temperature taken? Under what conditions or temperature range does the burner kick in to heat the water? If the thermostat is set to 130 degrees, what should the temperature be of the water at the bottom of the tank once the burner shuts off?
Given I now have a clean tank bottom with little sediment, where should I look next?
Thanks again for all the replies!
Edit: A little more feedback. We've had this problem since we bought the house a month ago. Two weeks ago I replaced the PRV and set it to 50 psi. A week ago I installed an expansion tank (WATTS DET-12). See picture below: