Probably a fuel pump check valve going bad. My 3.5 2001 300M does the same thing. There is a check valve on/in the fuel pump assembly that is supposed to maintain fuel pressure for the next start. If it leaks pressure off, you have no pressure for hot restart. My guess is that on cold start the computer sends an extra rich shot of gas and she will light off normally.
Test for you (that works on my 3.5), On a hot restart if it does not want to fire instantly... cycle your key completely off, then back on to start. This makes my 3.5 fire right off right away on the second attempt.
Your Intrepid probably has a drain plug on the bottom of the gas tank. This makes it easier to drain the fuel and drop the tank for fuel pump replacement. I have not replaced mine yet (104K miles) but the time is drawing near..., on my "to do" list.
My bet is a new fuel pump assembly will make it start like new when hot or cold.
That said, I'm not 1/2 as smart as Dave or Ron,
so do your checks, your experience may vary (official disclaimer)