sounds like time to replace 100% of the battery-->starter cabling, at the very least remove, inspect,clean, reattach. 16 years is a long time Could be as simple as the ground bolt being an 1/16h of a turn loose to not let enough electrons flow to the starter.
This is assuming you can here the starter solenoid 'click'. If it doesn't, check the control wiring. Could even be the ground on the solenoid.
Would need to see the wiring diagram but if 'heating it up ' makes it start,sounds like a connection is 'lost' when cold, reconnect when 'hot'.