A LR35's right engine Fire Warning alerted during climb out. When thrust was reduced the warning ceased so the flight continued normally and later a weak heat sensing unit was found to have caused the warning.

Narrative

In the evening after takeoff with 2 nurses and one patient on board; in the climb; the right hand engine fire warning light came on. Confirmed it was right engine with SIC (Second in Command); I pulled back power on the engine as the memory items require. As the ITT on the right-hand engine got below 800 degrees; the fire light extinguished. It was not on for more than ten seconds from noticing it until it went out. The checklist suggests bringing the engine to idle and flying on the other engine and land as soon as practical. However all engine indications were normal. After conferring with the SIC we decided to continue to our destination if the fire light stayed out with the engine at 795 ITT. The light did not come on again for the rest of the flight. We continued without incident for the rest of the flight. We had two good engines; and one malfunctioning indication system which malfunctioned once and did not reoccur. Two pilots made the decision to continue flight safely. The checklist can not cover every situation. In this case idling a perfectly good engine would have made the situation more difficult to deal with.