Get a new battery.It solves lot of issues with those allions/premios.If the original spark plugs has never been changed get new ones.Even though they claim to run for years you will definitely feel the difference of new spark plugs.
About the random heating issue can say that the radiator water pump is corroded or not working correctly.Random heating up issue Is a common symptom of a failed water pump.About the tire lock up think no idea.