Book Conceptual Physics by Paul G. Hewitt defines second law of thermodynamics as
"Heat of itself never flows from a cold object to a hot object"
Temperature is a measure of the average translational kinetic energy of the molecules in a substance.
What is heat?
The energy transferred from one object to another because of a temperature difference between them is called heat.
So, in theory, heat will travel from hot object to cold object till the average translational kinetic energy of both the object becomes same.
Now, look at the complete universe. If second law of thermodynamics would have been the only rule for changing the average translational kinetic energy, then the universe would be in equilibrium i.e. if you take any object in the universe, it would have the same average translational kinetic energy. Here I assume that universe is not expanding.
If universe would be expanding, then it would still be in equilibrium, but the temperature may go on decreasing with time.
As you can see, we can falsify both the statements by looking at our present knowledge of the universe.
Before we can go further, we have to understand that what gets transferred from hot object to cold object.
If you place a bucket of water in sunlight, the temperature of water increases. Similarly in the night, when there is no sunlight, again temperature of water decreases. So it is the electromagnetic light that changes the average translational kinetic energy of an object.
So, it nothing but the amount of electromagnetic light at a particular place determines, what will be the average translational kinetic energy of an object.
An object with more average translational kinetic energy will radiate more energetic electromagnetic radiation.
But why do, the universe is not at equilibrium?
It's because of rotation and revolutions of the object and also because the amount of electromagnetic radiation at any particular time or state of the universe is not constant.
Due to rotation and revolutions of the object, shadow (or hindrance) is formed in the way of electromagnetic radiations, so at a given place with the change in time, the temperature changes. An analogy can be our earth and sun.
The amount of electromagnetic radiation at any particular time or state of the universe is not constant because there is always an interconversion of electromagnetic radiation to dormant low energetic mass. (Einstein Equation (E=MC^2)
If you take entropy as the arrow of time ( the time I mean change of state of all the particles of the universe), then the definition of the entropy of disorderliness becomes fuzzy or wrong.