The answer to 'why is my P-trap no hot water' is that the P-trap is not connected to the hot water supply. The P-trap is the U-shaped pipe under your sink that holds water to prevent sewer gases from entering your home. It is typically only connected to the cold water supply, not the hot water.
If you are experiencing no hot water in your P-trap, it likely means there is an issue with your hot water supply or plumbing. This could be caused by a problem with your water heater, a blockage in the hot water line, or a faulty valve or fitting. In most cases, this will require the assistance of a professional plumber to diagnose and repair the underlying issue.