While what the other guys are saying is plausible, let's back up a step. What, if anything, was done to the car (no matter how unrelated you may think it is) before the problem showed up? Is this happening on the same load of fuel, or has it continued over more than two fills? Are you using any fuel "improvement" additives?

If the car ran well for 9 years it's unlikely that the fuel line routing is the issue unless something else has changed to now impact them. Keep in mind that vapor locking just about always occurs at the fuel pump (it's designed to pump liquid not vapor). Jim's comment about the filter could be true if there's a filter before the pump, while you're thinking it's temp related it could be time related and the filter becomes more restrictive after each startup. Likewise, if ther'e a "sock" on the fuel pickup in the tank, it could be getting plugged or collapsing as the fuel pump "sucks" in tank bottom junk. Once you stop the car for some period of time the "junk" sloughs off, only to be picked up again during the first minutes of use the next time. If it were the filter(s) after the pump, that would more likely be noticed at higher speeds rather than at idle or slightly above (fuel bowls can't fill fast enough to keep up with demand).