Do you mean when it is hot outside, but the engine is cold?

Then you might look at over enrichment during start. Someone with XJ6 specific engine knowledge can help you with what would cause this. It may be possible to diagnose this by seeing if it starts better with the gas pedal held to the floor.

If you mean, hot outside, and engine is hot. Then it is heat soak. The gas is forming bubbles in the fuel lines. Again, someone with XJ6 specific knowledge will help you with the specifics.

 

Jaguar made some mods to the fuel rail and pressure regulation arrangements on the Series 3, but I don't know what year, although it sounds like you have the old system. The mods were to do with fuel vaporisation in the fuel rail due to heat soak. Now of course, here in the UK, where I live, it is always cold, wet and miserable so I never had any trouble with my unmodified Series 3, but hot countries did, and as you live in Arizona, a very hot place in summer, you could benefit from the modification. As far as I remember, it was a temperature-sensitive valve that released pressure in the fuel rail and allowed the system to recharge the fuel rail with cooler fuel from the tank.