On some bad advice I had a new hot water heater installed and have the same problem.
2100sq.ft.house with 2 1/2 baths. Three people in the house. It takes 2 to 3 minutes
To get hot water at a faucet or any other outlet. Now I'm told that I need a thermal expansion tank between the main water line and the hot water heater. The cold water line to the hot water tank is very warm to the touch.

I hope you got a 50 gallon water heater. You said bad advice? How old was the previous heater? What size? Gas or electric?
If you are concerned about getting ripped off, call the bbb.

1- wait long time for hot water... home depot sells a recirculating system for $199.95. It is easy to install and solves that problem.
2- cold inlet pipe warm... heat rises
3- thermal expansion tank... a code revision not long ago required that an expansion device be installed on a closed system. Do you have a check valve after your water meter? If so, a device is required by code, it also protects your plumbing. The choices are a] thermal expansion tank, b] thermal expansion valve [my favorite] c] thermal expansion toilet fill valve.

Expanding on what Doug said. The recalculating system is the only real answer to long runs. I managed to relocate my water heater last summer and rearrange some to the piping to reduce the lengths of the runs.

When you add cold water to the tank, it expands as it heats and the excess has to go somewhere, either back out the cold water line or out the T&P valve. An expansion tank still allows it to back the cold water line if you have a check valve or back flow preventer.

Are you a plumber?