Easiest and cheapest the to check is for coolent on the oil.
The cutting off and starting 20-30 minutes later could be a blown head gasket; cutting off results from coolent in the cumbustion chambers, killing the spark. It re-starts after the collent has drained out.
Also.....look for steam (white exhaust) coming out the pipes for the first couple minutes after you start up the car.
Black 1996 Impala SS, MTI 396ci, Ported AFR 210 Heads,
Competition Cam 236/242 Custom Grind
58mm TB, Clear Image 1 3/4" Quad-1 Headers with 3" Cut-outs, DynoMax 2.5" Cat-back
Yank 3600 stall TC, 4.10 gears
Bryan Herter tuning = 419 rwHP @ 6250 and 450 rwTQ @ 3750
SR 398ci in the works