CRJ200 Captain experienced a L 14 DUCT message passing FL230 during climb and electecd to divert per QRH directives. During the diversion the FMC failed and ATC provided vectors to the airport. Upon landing; maintenance determined a loose wire caused the false warning.

Narrative

While climbing through FL180 we received a momentary L 14 DUCT message and then it cleared. We reviewed the QRH in the event the message returned and decided we could continue the planned flight. At approximately FL230 we again received the L 14 DUCT message and it persisted. We executed the QRH procedure and as directed made the decision to divert to the nearest suitable airport [which] was about 25 miles behind us. We notified ATC; declared an emergency and began the turn back. I notified Dispatch via the ACARs and asked them to notify the station. Upon returning to the navigation section of the FMS it displayed a 'FMS NOT AVAILABLE' message and the display on the MFD was blank. We asked for a vector to the airport; completed the checklists and conducted a flaps 20 landing. Upon clearing the runway the airport fire and rescue conducted a heat scan of the aircraft and we were advised that the scan was normal for our type of aircraft and we elected to taxi to the gate. Upon landing and a consulting with Maintenance Control it was determined to be a false warning caused by a loose wire in the loop connector.The only suggestion would be a revision to the QRH procedures to include all necessary checklists to the ground. The procedure had items to complete before landing that are not part of the normal procedures requiring a change between normal procedures that don't all apply to the QRH and back again.