Why and How heat energy is converted into kinetic energy?

Are you talking about
"why and how the heat energy of the particles is converted into kinetic energy?"

To answer this question, we first clarify the meaning of "heat":

Thermal energy (heat) is defined as the sum of kinetic energy and potential energy of random motion of particles in the reference frame of their center of mass.

Therefore, thermal energy (heat) is just another way to describe the kinetic energy and potential energy of particles. It is just a matter of different points of view. Macroscopically, for example, when a box of air is hot, we can say that it has a high thermal energy. But what does HOT mean here? When we look at the air microscopically, it is the motion of the air particles that gives you the feeling of hotness - the faster the particles move, the greater impulse (or force) of the air exert on its surrounding. This impulse (or force) gives you the sense of hotness. So, the faster the particles = the higher the temperature.

When we consider individual particles, we consider the motion (kinetic energy) of the particle. We cannot say the particle has certain heat energy. Heat energy is used to describe a collective kinetic and potential energy of particles. So, we DO NOT say the heat energy of the air is converted the kinetic energy of the particles. We should say the heat energy of the air IS the kinetic energy of the air particles.

The particles absorbed the heat supplied to them and they move faster. Since temperature is related to the kinetic energy of the particles, as a result, the absorption of heat energy is reflected in the rise in temperature.