I am glad to see young automotive enthusiasts who are also taking an interest in physics. If you want to simplify the coolant heat transfer it comes down to the following:
We will assume for the sake of simplicity that the engine puts out heat at a constant temperature (which should be roughly proportional to the power output of the engine) We can assume this to be constant. So we have what we call a constant heat flux boundary condition.
The engine block and the coolant exchange heat via a process known as convection (often called newton's law of cooling) q=ha(DT)v , where q is the heat flow in watts, h is the convective heat transfer coefficient, and DT is the temperature difference between the engine block and the coolant.
The coolant can be modeled as a flow which changes temperature via the formula q=mDotcDT_fluid , where mDot is the mass flow rate, c the specific heat of the coolant, and DT_fluid the temperature change of the coolant or it can be modeled as a aggregate mass via q=mcDT_fluid/timeElapsed , where m is the mass of the fluid, and time Elapsed is how much time has passed
the coolant has a transient (changes in time) warm up behavior and a steady state (constant) temperature (which is modulated by the thermostat in the car)
coolant temperature and temperatures in an internal combustion engine in general are very complex studies, but they can be greatly simplified to make for a simple overview of the problem
If you are interested we can exchange emails and I can help you out a bit more. You can even use my paper on heat transfer as a source since the problem is fairly similar to what I am working on in my research. I also have some log files off my subaru which you can use to makes some graphs. You could try to compare newton's law of cooling to the data from the logs.
I am an engineering masters degree student with emphasis in heat transfer and an avid Subaru enthusiast ( I am currently learning engine tuning)