Thermostat opening?
take it the fan goes on when shorted out but not when pluged in as normal? (replace fan switch)
earth the plug for the temp guage sender...does it now go right up to the top on the guage? if so, replace temp guage sender. their only a few bucks, as is fan switch.
header tank cap in good nick? not leaking?
Fan should stay on with ignition, not when keys are out.