Well, before you start throwing money at it, you should compare the price of the PIP to the ignition module.
The ignition module is about $60, while the PIP is less than $30.
Of course, the ignition module is likely easier to replace as it does not involve pulling the distributor out and tearing it apart. But, the PIP is a much more common failure on these cars IMHO.
PIP failures are certainly heat related as well. The single most common example of a failing PIP is that the car is started, it is driven until it reaches temperature, and then the car dies and will not start. Later, after the passage of some time, the car magically starts. Not because anything fixed itself, but because everything cooled down.
So, while it may in fact be the ignition module, I have never actually heard of someone replacing that part and having their no start issues fixed. Usually, replacing it is followed by something along the lines of "this damn car, I have spent all of this money on parts, and it is still messing up!!!!" How-To: Rebuild Your Distributor and Replace the Stator
2006 GT - Vortech polished w/ intercooler, Eibach suspension, Hurst short-throw, some other goodies - tuned by Paul's High Performance. It moves...
and it collects dust admirably while parked for repairs in the garage...
SOLD - 1995 Black Mustang GT, AODE. Loved it, but I had to let it go...