it will die and won't start up again until the engine cools off?

possible crank sensor going out,or a bad ignition control module.You can have the control module tested at your local parts store.

I agree with DennyP they had problems with the crankshaft sensor here is how to change it out to fix the problem. Check the images below:


REMOVAL:

1. Disconnect the serpentine belt from the crankshaft pulley.
2. Raise the vehicle on the hoist.
3. Remove the right front tire and wheel assembly.
4. Remove the right inner fender access cover.
5. Using a 28 mm socket, remove the crankshaft harmonic balancer retaining bolt.
6. Remove the crankshaft harmonic balancer using tool J-38197.
7. Remove the foreign object deflector (DO NOT use a pry bar).
8. Disconnect the sensor electrical connector.
9. Remove the sensor and pedestal from the block face.
10. Remove the sensor from the pedestal.

INSTALLATION:

1. Loosely install the crankshaft sensor on the pedestal.
2. Position the sensor with the pedestal attached on tool J-37089.
3. Position the tool on the crankshaft.
4. Install the bolts to hold the pedestal to the block face, torque to 30 Nm (22 lb ft).
5. Torque the pedestal pinch bolt to 4 Nm (35 lb in).
6. Remove tool J-37089.
7. Install the foreign object deflector.
8. Place tool J-37089 on the harmonic balancer and rotate the tool. If any vane of the harmonic balancer touches the tool, replace the balancer assembly.
9. Install the balancer on the crankshaft.
10. Apply thread sealer GM # 1052080 or equivalent to threads of the crankshaft balancer bolt. Using J-36660 Torque Angle Meter, torque the bolt to 150 Nm + 76 degrees (110 lb ft + 76 degrees).
11. Install the inner fender shield.
12. Install the tire and wheel assembly. Torque lug nuts to 140 Nm (104 lb ft).
13. Lower the vehicle.
14. Install the serpentine belt.


Check out the images (below). Let us know if you need anything else.