Technically, the internal kinetic energy is just called "internal energy" or sometimes "thermal energy".Heat is the internal kinetic energy associated with thermal motion of atoms and molecules, that flows between bodies at different temperatures.
The term "heat" tends to be reserved in Physics these days to describe energy that is transferred from a hotter body to a colder one, due to a temperature difference between them. This is distinct from "work", which is a transfer of energy due to the action of forces between bodies.
Thus, objects can't be said to "have heat". They "have" thermal energy, or internal energy. They can transfer heat to other things. They can also do work on other things by exerting forces.