Is energy related to work or is it an entirely different thing? I was reading about work done and energy, and I got to know some things. Let's take a simple example:
Suppose I move an object to a certain height. Here, I apply a force against the force of gravity to move the object, and by definition, I do work on the object, which means I am transferring some of my energy to the object. This case is crystal clear to me.
Now I cannot understand the case of heat transfer. I read that when something's temperature rises, it is said to have more energy. And if it comes into contact with something cold, it transfers some of the heat energy to it until both objects have equal energies. Are the particles applying any force in this case against any force? If not, then why this is said to be an energy transfer?
 A: First, it's not until they have equal energies. It's until they have equal temperatures. Be careful because while temperature is proportional to the internal energy of a body, it's not the same.
When particles have heat, they vibrate. You can imagine a solid body as a system of spheres bound together with springs, and all these vibrate together. This is a very successful model in basic solid state physics. 

Now based on that, you can imagine that if you get to solid state bodies in contact, the boundary particles will transfer their kinetic energy to the other body's particles and get them to oscillate, until the both systems reach equilibrium.
I have to say: While this picture is valid only for simplicity, it's much more complicated in reality.
A: Yes, in order to transfer energy you need something energetic to travel (like in radiation) or you need to do work on something. When a hot body is in contact with a cold one, the average effect of collisions between their surfaces is work done on the cold body.
A: Verbally, energy can be defined as the ability to do work, or as a potential to carry out work.  But energy is not work.  Consider a simple case when a single body moves in constant speed in an empty space far away from any other mass – meaning there’s no any gravitation force surrounding that body.   Obviously that moving body has a Kinetic Energy, but that body is not performing any work, because to do work a force must be applied.  But the body cannot apply any force on an empty space and that’s why it’s not doing any work.  It will do any work when it will bump another body and thus a force will be applied.  
As to your question about Heat Transfer and Force, the answer is YES.  Approximately speaking, in Heat Transfer, Kinetic Energy is transmitted from the atoms of the hotter body (atoms vibrating faster) to the atoms of the colder body (atoms vibrating slower).  It means the atoms of the hotter body are bumping with the atoms of the colder body and thus each of the atoms is applying force on its counterpart and doing work.  As a footnote, it should be noted that in order to produce work it also requires that a force will be applied along with a displacement caused by that force.  When we just stand on the earth and apply force with our weight, it’s not considered work because there’s no displacement, neither of the earth nor of us.  
