Car shuts off while driving and will start back up when it cools down

I could be driving at any speed and the car will just quit running. It will also shut off when I slow down and idle. The car has a slow oil leak and has always idled high. I have to put in in neutral to prevent it from shutting off but that works only fifty percent of the time. No smells or unusual sounds. Had a new battery installed a month ago. Alternator was checked twice and it is fine but will need to be replaced next because of the sound the bearings are making. Mechanic hooked up to diagnostic machine and no codes came up. Had fuel filter replaced and still have the same issue. No warning lights illuminate.