If it were your SAP, it would ONLY last about 90 seconds after a cold start-up. That's
it! If it is possible it is your fan clutch (do search about rolled-up newspaper) your fan blades could come up right through your hood, destroy radiator, and more. At least see if you can easily stop fan blade on a cold start-up in morning with just a small amount of rolled-up newspaper. If you can't stop your fan blade easily right upon cold start-up, your fan clutch is NG. Then you'd be driving with time bomb ticking. Do not race over about 3000 rpm if you find fan blade clutch is shot.