2001 Mazda Miata OBD II code P1345 Stalled when hot cooled runs again, any idea what is wrong?

On the way home from the car lot I bought it from; (after the as is no waranty breifing) highway, cruising 75-80, fifth gear AC on, 88 deg outside temp, misfires a couple of hichoughs then no throttle at all, pull over, turn off radio and AC, Check eng light is on, idles but any throttle and it stops running ease throttle and it idles again. coolled for 5 minutes while I opened the hood to check oil and h20 levels (both guages read ok and both were fine.) drove fine at 65-70 till I got to gas station (off chance fuel gage bad I fueled up 8.9 gal.) Code p1345 Manufacture ignition, I am hoping there is more specific guidence out there. Thanks