Holding the gas pedal down(opening throttle plate to let more air in), dries out any coolant that may have entered cylinders from bad gasket, so it would explain it.
But no on the MAF sensor, engine will start fine and run without MAF sensor connected, just won't drive well.
On V6 engines the ECT(engine coolant temp) sensor(2-wire) should be located next to the Thermostat housing.
The dash board's temp gauge sender(1-wire) is often right next to it.
On some 3.0ls there might be a metal "T" pipe by the water pump and the ECT sensor will be on it.
This page shows 2000-2005 3.0l ECT sensor next to t-stat housing:
| Repair Guides | Component Locations | Coolant Temperature Sensor | AutoZone.com
For start up Computer only sees 2 gas pedal positions via the TPS(throttle position sensor), under 1 volt(foot off the gas pedal, injectors on) or over 4.5volts(foot to the floor, injectors off).
1/2 throttle would just be like foot off the gas pedal, although it would let more air in to dry out cylinders.
Although unlikely, an injector could be leaking causing a flood effect when engine is off.
After engine is warmed up shut it off then remove intakes air plenum and open throttle plate, if you smell a strong odor of gasoline then fuel is leaking into the warm intake and vaporizing.
I doubt you could crack the block but........??
Heads crack pretty easy.