SHBell, try this, when attempting to start the car when hot, turn the key to the RUN position and let it set there for a few seconds (5 or so). Do not take it all the way to START, but only to RUN. This will prime the fuel system. Then rotate the key the final position to start the car. If the car starts after doing this, then you are more than likely looking at a bad fuel pressure regulator. Could be a problem with a bad fuel pump though too bleeding down back into the gas tank.

Let me see what else I can come up with.

 

SHBell, no relay, but there is a control module for the fuel pump. It is located right behind the rear seat (in the trunk) on the driver's side of the car. If you access the module, you will want to find the red wire and yellow wire. Verify that you get 12 VDC across these two wires when the engine should be running. If you are getting 12 VDC there but are not getting fuel pressure, then that confirms a bad fuel pump. If you are not getting 12 VDC, then verify that you have 12 VDC between pins 9 (positive) and 2 (ground). If you don't have 12 VDC, then you have a bad fuse or a wiring problem between the fuse box and the fuel pump module. If you do have 12 VDC, then that confirms a bad fuel pump control module.

Hope this helps.