A319 brake temperature indicators show one brake hot upon gear extension for landing. After landing inspection determines it to have been an apparently false indication.

Narrative

At landing gear extension; outboard left main temperature showed in excess of 730 degrees C. With all other brakes normal; there is no quick reference handbook procedure for hot brakes inflight. We broke off the ILS and flew around with gear down and brake fans running. Temperature on hot wheel slowly decreased. Used ACARS and communicated with Dispatch and spoke over the radio with Mechanic via phone patch. It was believed to be an erroneous temperature indication. Asked Tower to have crash fire rescue equipment standing by just in case the brakes truly were that hot and may have caused a fuse plug to melt. We did not declare emergency; but Tower closed the airport when we landed. Fire Commander asked us to clear the runway and shut down engines so they could inspect aircraft. Everything appeared normal; taxied to gate; airport reopened after being closed. About 15 minutes later; aircraft sent to hangar for maintenance. Question: Will the LGCIUs monitor brake temperatures while the gear is retracted? Seemed odd that we had no warning of a hot brake until the gear was extended as if they were unmonitored. That sure wouldn't be very good design. I would want to know of an overheated brake and get it out in the breeze to cool off.