Sheep Guts,
The KingAirs you mention were not fitted with thermal loops but Infra Red light detectors. That's why a glorious red sunset/sunrise would trigger the engine fire warning, because the light entered the engine cowls.
The 'fix' for this (though it wasn't a 100% fix) was to fit a steel cresent plate to the exhaust flange to reduce the chance of light entering via the gap 'twixt cowl and jet pipe.