What actually is a force?

So, is temperature difference here the force? Is force at its core an energy transfer/interaction?

Do not forget that force is a vector quantity, whereas energy is scalar. So temperature difference cannot be a force. This site might help in understanding force.

which for fixed mass can be seen as F=dp/dt ,

Is force at its core an energy transfer/interaction?

It is a momentum transfer interaction, and in classical mechanics connected through the size of velocity with energy.

You ask in another answer:

How by increasing temperature, am I increasing the velocity of this molecule?

Temperature is an intensive variable:

An intensive property is a bulk property, meaning that it is a local physical property of a system that does not depend on the system size or the amount of material in the system. Examples of intensive properties include temperature, T; refractive index ...

The individual particles in the material with a given temperature T do not have temperature, they have kinetic energy, and they have momentum.

You ask:

Like how am I changing its direction by introducing a change of temperature? If it's not the temperature difference, that is doing it directly, then what is?

The way temperature is related to kinetic energy in statistical mechanics

is not directly, by through the average kinetic energy of the particles in the medium studied.(the bar over the kinetic energy of the molecule means: average)

And it is the average kinetic energy that can be associated with a molecule. Heating a gas will raise its temperature , and thus the average kinetic energy, but the individual particles will be scattering randomly with various kinetic energies.

So there is a causal connection between raising the temperature and the kinetic energy of the individual molecules, but the connection is not direct, it is from a bulk property to an average of a property describing individual particles. It is not a one to one effect.

is temperature difference here the force

Force is proportional to acceleration, while temperature is function of velocities of particles, not their accelerations. This is similar to difference between force and momentum. Momentum/temperature captures the state of the system, while force captures how is this state changing. So there is big difference

Is force at its core an energy transfer

No it is not. When you have rock standing on the table, the force of gravitation is acting on it, but because it is compensated by the reaction force of the table, the rock is static and no energy transfer is happening.

Addressing the question in the comment:

How do you know that the gravitational force isn't supplying the rock with energy while the reaction force is removing energy at the same rate?

The rock in its rest frame is acted on by two forces of equal magnitudes but in opposite directions. The problem is how would you decide which of the two is supplying the energy and which one removing it? Energy, being scalar quantity, has simply too little information to address this problem.

The first law of motion states that anything that creates a change in the rectilinear motion of a particle is a force. This is, however, only true in an inertial reference frame; in fact, this can be thought of as defining an inertial reference frame.

Temperature isn't a force, it's just a macroscopic phenomenon that has to do with microscopic forces.

Consider the following thought experiment to understand what a force is: You have an object attached to a spring whose other end is fixed and the spring-object system is in space. If you stretch the spring and release it, the spring will move the object in some manner. Now if you stick an identical object to the first and stretch the spring and release it in the same manner, the spring will move the pair of objects in some way that's different from how the spring moved the single object. Then you say to yourself "Well, the spring is pushing/pulling the objects and it seems reasonable that the strength and direction with which the string pushes/pulls doesn't depend on the objects attached to it per se, rather it depends on how stretched/compressed the spring is. I suppose that I can perhaps assign a number and direction to the push/pull of the string. Oh, and suppose I say that the first object has a quantity associated with it called its mass. Well then the second object---identical to the first---has the same mass. And let's suppose that the mass of the two objects combined is the sum of the constituent masses."

And you'd run some experiments and conclude Newton's second law: $$a propto frac{F}{m},,$$ acceleration is proportional to force divided by mass. Because the force and mass are just some numbers you pulled out of your butt, you can define the constant of proportionality to be 1 thereby making Newton's second law $$a = frac{F}{m},.$$

And you say to yourself, "Well isn't that dandy?! The assumptions I made earlier are useful for computing accelerations! For if I have an object attached to my spring and it has an acceleration of 2 meters per second per second when the spring is stretched/compressed by a certain amount, I know that if I append another object identical to the first to the end of the spring, the acceleration when the spring is stretched/compressed by that same amount would be 1 meter per second per second!"

And that's my best description of what a force is; you go for the intuition and you stay for the objective, empirical results.

Energy works similarly to force: You define some fancy physical quantities to be energy (e.g. some formula involving an electric field) and it happens that if you do so you get a nice description of reality in which energy is conserved.

Temperature is not a force, not because it is a scalar quantity (that's like answering "because the units of measurement differ"), but because of the concept of force.

A force is a cause which effect produces spatial change of motion, evidently, change of motion of an object, as perceived by a subject. In case of temperature, objects do not change motion with temperature (in standard conditions, that is, the rock keeps being what an observer would call "the same thing" before and after the change).

Evidently, --in standard conditions-- the change of temperature of a thing changes the motion of its molecules. But that's not the movement of the thing, and that's not the change of temperature of molecules. Temperature applies to the thing, not the molecules.

In simple words, there are no "hot molecules".