Well, strictly speaking, you can not heat an individual atom, because heat is a macroscopic phenomenon: it is a mechanism of energy transfer from one macroscopic body to another one. And the same is true for the related notion of temperature.
But, both temperature and heat can be explained at microscopic level as follows.
Particles that constitute bulk matter are in constant random motion and temperature is nothing but a measure of the mean kinetic energy of particles random motion. Heat then can be understood as macroscopic manifestation of transfers of this kinetic energy of random motion from a statistically significant number of particles of one body to particles of another body.
Thus, you can heat a body (not an individual atom), i.e. you can transfer energy to it by means of heat, and while the body is heated, the mean kinetic energy of all particles (atoms, nuclei, electrons) will rise, i.e. it temperature will rise.
The kinetic energy of an electron acquired then can be partly redistributed with its potential energy when electron ``jumps'' into higher orbital. After excitation the atom may return to the ground state or a lower excited state, by emitting a photon with a characteristic energy.
And, of course, in principle, we could add so much energy to a body be heating, that electrons will indeed leave atoms.