where is the exhaust temperature sensor located
There is no exhaust temperature sensor. There are at least two O2 sensors in the exhaust system. Some systems use the first or up stream to regulate the fuel mixture and the second or down stream sensor determines the health of the catalytic converter. Some systems use both sensors to determine the fuel rate. V6 and V8 engines may have O2 sensors in each header.
When it quits, check for spark. Could be the ignition coil breaking down when it gets hot. Sometimes they do that. Also, if the fuel system has been altered, check that you're getting fuel to the carburetor. It may be vapor locking. Check this when it quits as well. HTH. -Jim