Engine won't shut off

[humayun.chughtai.7]

Recently, i bought a toyota echo hatchback (same as vitz/yaris) 2001 UK Import. The car is in great condition otherwise. It is original 1300 cc with 2NZ engine in its bay.
Now the problem comes up daily in the morning time or whenever I start the car after an interval of 4-8 hours. When I start the engine, red over-heat light glows up in the cluster. During this light in the cluster, if I turns the key to ACC position to turn off engne, it refused to turn off while all the electronics of the car shuts off except engine and when I turn the key from ACC to LOCK position, the self-starter kick-in within the running engine producing a loud karrr-karrr sound. So I again turned the key to ACC position and Thank God, the starter turns off back, while the engine is still running.
This problem only happens when the engine is cold and red over-heat light glowing in the meter. After 2-4 minutes, that light goes off and everything is just as fine as nothing happened. Now I am very tensed about this weird issue. Kindly help me.
With Love from Pakistan <3