Not long at all...a few minutes max.
You'll find the temperature differs depending on where it's placed...front to back (back is colder) and top to bottom (bottom is colder).
I would say thirty mins if the answer is not what you want
( you know if it is 4'C after 5 mins, then fine it is working. If it is 8'C after 15 mins I would still wait longer before taking an ax or sledge hammer to it )
Of course, the best time to trust a reading is first thing in the morning, when the fridge has been closed for a long time.
Only then should you consider adjusting the control slightly to make it colder or less cold.
You can buy fridge thermometers which are encased in clear plastic to slow down the rate at which it reacts to temperature changes like opening the door.