grand marquis 2001 engine stalls

We have a 2001 grand marquis that stalls while running. The temperature light on the dash turns on, check engine light also turns on and the car stalls. I put the car on neutral and restart it, runs well for a while and does the same thing over and over. The car has been scanned but nothing comes up. What can it be?

Here is some information for you. Believe it or not, the Coil on Plug ignition system can cause this problem. Here is an OASIS report on the issue. I was going to post the TSB, but it is very long and has lots of charts that may not show. So I have highlighted the TSB in red for you. Hope this helps.
19183 1998-2005 MULTIPLE VEHICLES - WARNING LIGHTS FLASHING - TEMP GAUGE PEGGED HOT OR COLD - TACH OR SPEEDO BOUNCE - DRIVEABILITY CONCERN - UNEXPLAINED DTC'S
SOME 1998-2005 VEHICLES EQUIPPED WITH A GAS ENGINE THAT USES A COIL-ON-PLUG (COP) SYSTEM MAY EXHIBIT ONE OR MORE OF THE FOLLOWING CONDITIONS DUE TO RF INTERFERENCE ON THE SCP/CAN NETWORK: ABS LIGHT FLASHING, A FLASHING FAIL SAFE COOLING LIGHT, TRACTION CONTROL LIGHT FLASHING, INTERMITTENT 'BUMP'(MISS), TEMP GAUGE PEGGING HOT OR COLD, TACH OR SPEEDOMETER BOUNCE, BUCK/JERK AT CRUISE, AND/OR UNEXPLAINED CODES. THERE ALSO MAY BE AN INTERMITTENT LOSS OF RPM. PRIOR TO FOLLOWING NORMAL DIAGNOSTICS FOR THE SYMPTOM, USE TSB 05-22-08 TO DETERMINE IF THERE IS A CONCERN WITH A COP. MONITOR POWER BALANCE TO SEE IF A CYLINDER IS DROPPING OUT DURING CONCERN. IF POWER BALANCE CONFIRMS A CYLINDER DROPPING OUT AT THE TIME OF THE CONCERN, PERFORM THE COP STRESS TEST FOR THE SUSPECT CYLINDER'S COIL TO VERIFY INTERNAL COIL SECONDARY FAILURE.