What was found
LGA TO IAD - DEPARTED LGA AT TAKEOFF POWER, AT APPROXIMATELY 300 FT AGL ENGINE NR 1 HAD AN ITT OF 950 DEGREES. WHEN ENGINE POWER WAS REDUCED, ITT LOWERED, BUT WAS STILL AROUND 900 DEGREES. AT 1,000 FT AGL, RECEIVED FIRE WARNING INDICATION FOR ENGINE NR 1. ENGINE NR 1 WAS SHUTDOWN AND THE FIRE INDICATION QUICKLY EXTINGUISHED. RETURNED TO FIELD WITH UNEVENTFUL LANDING. MAINTENANCE INSPECTED AND RAN ENGINE AND FOUND A CRACKED BLEED DUCT NEAR THE HIGH PRESSURE SWITCH. MAINTENANCE REPLACED THE CRACKED BLEED DUCT, PERFORMED HIGH POWER ENGINE RUNS AND OPS CHECKED GOOD.