What was found
CLIMBING THRU 3000 FT, RT RED OIL PRESSURE ANNUCIATOR ILLUMINATED WITH A MASTER WARNING. RT OIL PRESSURE GAUGE WENT TO ZERO. INITIALLY OIL TEMP GAUGE WAS IN NORMAL RANGE, THEN UNABLE TO CAPTURE OIL TEMP READING. BURNING ODOR IN CABIN WITH NO VISIBLE SMOKE. PERFORMED PRECAUTIONARY SHUTDOWN ACCORDING TO EMERGENCY CHECKLIST. ON POST FLIGHT STILL HAD BURNING ODOR OUTSIDE THE ACFT AND OIL WAS IN ACCEPTABLE RANGE ON SIGHT GAUGE. NO OIL DRIPS NOTICED.