Osama, this may possibly vary according to individual cooling system designs, but my experience has been that there are certain common factors at play.

Thermostats, located in upper parts of the engine block cooling water passages, where the upper hose from the radiator is connected to the block, are quite standard, I have found. They indeed throttle, as you say. They are not just on or off. Conversely, the now common electrical cooling fan, or fans (some cars have two) is/are on or off. It or they are controlled by a temperture sensor inside the radiator, probably the bottom part of the radiator. A simple two-pole switch.

What seems to be the case, among many brands of automobile, is that the electrical cooling fan only comes on if the thermostat is fully open, and the water temperature is still rising. Then the fan comes on. As the radiator water temperature cools, the fan shuts off. It will cycle that way, as long as you're stuck in traffic.

And it does not take much steady forward speed before the electrical cooling fan shuts off and stays off, as the car's forward motion creates enough of an air flow through the radiator fins. Even on warm days. No doubt, in extreme heat, or if the engine is operating at full throttle and heavy load, the fan's switch just might switch on and remain on. But in such cases, the engine is being overstressed and is likely to overheat. There's no adjustment going on anymore. Any equilibrium you might find is going to be unstable equilibrium.

In traffic, on warm days, you might just witness the electric fan coming on and shutting off, giving you a water temperature curve like the one in your diagram. Pick up some steady speed, and my bet is, the sinusoid curve will not exist anymore, as the fan shuts off and the thermostat does all the temperature regulating job.

The frequency of the curve you drew should increase on warmer days, in traffic, because the water temperature will more quickly keep reaching the turn-on point of the fan's thermostat switch. Fan runs, water cools, switch fan off, water quickly warms up, fan soon comes on again. I would expect the amplitude to increase slightly, but the frequency to increase noticeably, in warmer weather. While the electric fan is cycling that way, the coolant thermostat is wide open. Pick up speed, and the sinusoid should disappear, as the electric fan stays off and the coolant thermostat begins to throttle.

Cars with accurate, and not overly damped, thermometer gauges should show this behavior very clearly. They will also clearly show how on cold days, even if in traffic, the water temperature will not cycle up and down, and the electric fan or fans stay off.

Thanks Albert, I am pleased to get your support in this topic and appreciating your elaborated response. To be sure that I fully captured your valuable answer, let me repeat:

Quot: "Thermostats, located in upper parts .............. radiator. A simple two-pole switch" ...This part tells us that two parallel mechanisms are working together to regulate the temperature of the coolant (and accordingly the engine metal body temperature)

- One of them is a continuous action type: it is the throttling thermostat which has a moving plunger to continually regulate the flow rate of the coolant in proportion with its temperature. If the coolant is too hot, the thermostat will fully open. If the coolant is too cold, the thermostat will fully close, intermediate coolant temperature will result in a partially open (or partially close) thermostat !

- The second is a switching (ON/OFF) action type composed of the simple two pole switch (s) and the electric Fan (s) (yes ...most modern vehicles have two fans and their operation is somehow coordinated), and it is quite logic that the later has a cut-in and cut-out coolant temperature setting for switching ON/OFF the fan(s) respectively.

- The combined action of the two systems provided that they are both working healthy is to approximately fix the coolant temperature (and the engine metallic body temperature accordingly at a predetermined favorable temperature) and this temperature may vary only in a very narrow band (virtually) and this band is somehow independent of the ambient temperature, the driving speed, etc (In analogy to an electrical switching mode supply, It is quite logic that a PWM frequency (ON/OFF fan frequency) and duty (Fan ON intervals) may vary widely in response to a variable DC input (heat flow rate allowed by throttle) to give a fixed DC output (coolant temperature)

You are completely true in your diagnosis here:

Quot " Cars with accurate, and not overly damped, ..........fan or fans stay off." I myself witnessed the same in this car when I fit it with the regulating thermostat. The dial on the dashboard is held almost fixed once the car is warmed up irrespective of speed and ambient temperature!

My question above assumes that the vehicle is for some reason missing the continuous regulation action (the throttling thermostat is intentionally removed or stuck-open) and hence the variation band in temperature is widened due to the ON/OFF cooling action of the second system. Also the fact the hysteresis band in the coolant temperature and in the engine metal may not be in perfect compliance should be considered (recall that fans cut-in and out are activated by coolant temperature, while the attached profile is representing the temperature at a specific point on the engine metal body).

This paragraph is exactly what I am searching for its counterpart but in a different setup:

quote " The frequency of the curve you drew should increase on warmer days, in traffic, because the water temperature will more quickly keep reaching the turn-on point of the fan's thermostat switch.................., and the sinusoid should disappear, as the electric fan stays off and the coolant thermostat begins to throttle."

The different set up is : same or even warmer day, coolant thermostat (coolant throttle) is intentionally removed, high driving speed!

Thanks for your continued support

If the throttling thermostat from the engine block is removed entirely, on a very warm day, at least in traffic, the electric fan or fans will do the same job as with the throttling thermostat in place. Because either way, the throttling thermostat would be wide open.

But when the car starts moving so that airflow through the radiator is substantial, then the coolant temperature will start to drop, even on warm days, and the electric fan will go off. (I mean, engine coolant temperature should be quite a bit higher than the ambient temperature, even on very hot days. So you will always get heat conducting away from the radiator, to ambient air.)

Without that throttling thermostat in place, the coolant could potentially drop below the ideal running temperature for the engine. There is nothing to control the coolant temperature, so it will find whatever equilibrium, according to ambient temperature and power demands on the engine. No telling what that will be. And, since the cooling fan is not a factor when the car is moving, there should not be any sinusoid curve to describe the coolant temperature. At least, not caused by a cycling electric fan. If there is any sort of sinusoid, it would be caused by sinusoidal demands on engine torque.

Thanks, this is quite valid.