I hate to be a party pooper, but removing the air filter or drilling holes in it is totally pointless, unless you can keep the engine bay hot air away from it.
as Alex at RS barn will tell you each 10 degrees of air temp getting hotter will sap you of about 5-10 bhp if you use the holes without an airbox shroud you will loose power, if you use a cone filter you will loose power,
for max efficiency and power you want the air as cold and as dense as possible, one reason the turbo / super charger brigade use intercooler's, to get the charge air temp down,
I am sure with a little research you will find the air temp formula correct,
and Alex at RS Barn is the only person I know with a NA 968 over 300 BHP.
the hot start issue will be caused by the pressure retaining valve in the fuel pump, if the fuel pressure drops off to quickly when the engine is very hot the fuel boils in the injectors crating a vapour lock (from the Bosch Fuel Injection Manual) the car will not start on vapour.
I would get you service guys to change the fuel filter and the pump retaining valve that should fix that problem