$$He \longrightarrow He^+ +e^- \ \ \ \ \ .....\Delta H_1$$
$$He^+\longrightarrow He^{+2} +e^-\ \ \ \ .......\Delta H_2$$
We know $\Delta H_2$ by the Bohr's model of H-like atom .
Ionization energy of a H-like atom with atomic number $Z$ is $\Delta H_2=13.6Z^2/n^2$ ($e^-$ initially in $n^{th}$ orbit)
Also, $\Delta H_1 +\Delta H_2=79\text{ eV}$
So, we can get $\Delta H_1$.
Even though photons have zero rest mass, they carry a finite amount of energy and momentum.
A photon's energy & momentum is given by,
$$E = h\nu\space,\space \space p = \frac{hc}{\lambda}$$
where $\nu$ and $\lambda$ are frequency and wavelength of the photon respectively.
If the photon is absorbed by an atom and not re-emitted, the energy of the photon is completely transferred to the atom. These kind of collisions are inelastic. The atom takes up the energy as kinetic or vibrational energy.
If a new photon is emitted immediately after photon absorption with the same energy as that of the incident photon, the overall collision is said to be elastic. There won't be a change in energy, however, changing momentum is allowed.
However, sometimes, the emitted photon doesn't necessarily have the same energy as that of the incident photon and this kind of collusion (overall process)is also called inelastic collision.(Raman Scattering & Compton Scattering)
This missing energy is taken up by the atom as kinetic energy or vibrational energy.
The answer is highly simplified. The energy gained from the photon could be used for other purposes such as pair production of particles, knocking electrons off, etc. Also, the mechanism of absorption and emission are a bit complicated.
References: Photon-Atom Interactions - MIT OCW
Best Answer
Your question confuses two physics frameworks, the classical thermodynamic one, where the variable "heat" is defined, and the quantum mechanical where atoms with their nuclei and electrons are modeled.
In the classical framework temperature is related to the average kinetic energy of the atoms and molecules composing a substance under study:
Average means that there is a distribution of kinetic energies with which the atoms and molecules move bouncing against each other:
Here is how higher temperatures have higher fractions i.e. number of molecules at high kinetic energies.
The y axis is the fraction of molecules with that kinetic energy. Emin is the temperature at which the molecules of a liquid contain enough kinetic energy to change phase, from a liquid to a gas.
For higher temperatures there will be an Emin for a change of a gas into a plasma , the energy of collisions being enough to separate electrons from the nuclei.
There will always be enough energy in the tail of the distribution for some collisions to be able to ionize an atom or molecule. The energy is the difference in the energy levels to the ionization level, as seen here (second page) for hydrogen.
The temperature at which a specific gas will ionize into a plasma depends on the ionization energy and statistically the phase transition to plasma ( i.e. ionized gas) depends on the substance. Qualitatively phase transitions versus temperature and pressure are seen here:
The plasma phase is important in studies of astronomy.
To summarize , heat is a thermodynamic quantity and is only statistically connected to temperature , which is statistically connected with kinetic energy, and it is kinetic energy distributions which will show if there are enough atoms/molecules with kinetic energy equal or larger than the ionization energy ( a quantum physics quantity) to make a difference. There will always be at a given temperature some molecules with enough kinetic energy to ionize some atoms, but this is in a tail of a kinetic energy distribution. (Do not forget that a mole contains about 10^23 molecules).