the key does get hot because in your car the contacts cluster is not very well made. Leave it like that, if you feel the need to lubricate the lock barrel - get some beeswax, heat it and apply some to the key blade and move it in the ignition, blow it out with an air duster first - make sure you dont push the frosty liquid in there. If you cannot find the wax then some graphite powder is best - under no circumstances use WD40 or similar in there as it will jam the mechanism over time when the oil becomes sticky - oil attracts dirt.
btw - how come your shaft rusted? did water contact it? or is there a humidity problem in your car?