Two of the four showers in our house have the same problem. Some days
the water is hot and fine, but some days the water is just luke warm
and not comfortable for showering.

When the shower water is luke warm, nearby sink continues to provide
hot water.

The shower components are Delta make and the controller is a plastic
knob. http://www.deltafaucet.com/bath/details/1348-WS.html

We have two heaters on the attic and we believe both of these showers
are fed by the same heater. We don't know for sure.

The plumber that looked at the problem quickly diagnosed it to be a
problem with the cartridge. He did so without doing much analysis. I
read up on the cartridge and I am not fully convinced that replacing
cartridge will resolve the issue - but I am new to all this. Since we
recently had an expensive plumbing repair in the house, I really don't
want to spend time and money for experimentation.

I am only looking to see if you all agree with our plumber's
diagnosis. Thank you very much for your time and help.