the sun - Relocation to Mars

As it gets older, the core of the Sun starts to fill with Helium ash. This increases the average mass per particle and hence the core temperature must increase to maintain the pressure. This increases the nuclear reaction rate and the Sun becomes more luminous, at almost a constant surface temperature.

The habitable zone is controlled not only by the luminosity of the star, but also by the atmosphere of the planet. It's doubtful Mars would ever become "habitable" in that sense (without our intervention), but what I will assume is that you want the equilibrium temperature to be warmer than 263K, but say cooler than 303K (i.e. between -10 and 30 Celsius).

The details of finding the blackbody equilibrium temperature can be found here. The formula we need is
$$ T = left(frac {L_{odot} (1-a)}{16pi sigma D^2}right)^{1/4},$$
where $L_{odot}$ is the luminosity of the Sun at any time, $D$ is the distance to the planet, $a$ is the albedo and $sigma$ is the Stefan-Boltzmann constant. $T$ is in Kelvin.

I will assume that the average albedo of Mars is 0.25 (though it varies considerably with wavelength, depends on icecap coverage etc.) and that $D=2.27times10^{11} m$.
We can then rearrange the formula above to give the luminosity of the Sun for a given equilibrium temperature.
$$L_{odot} =21.3 pi sigma D^2 T^4$$
This means that for $T>263 K$, then $L_{odot}>9.35times 10^{26} W$, but for $T<303 K$, we require $L_{odot}<1.65times10^{27}$ W$. That is the Sun's luminosity should be somewhere between 2.44 and 4.30 times its current luminosity.

The next step is to look at a stellar evolutionary model for a star like the Sun.You can generate one here. I find that the Sun will have a luminosity in this range from ages 8.9 billion (at the cool end) to 10.0 billion years (at the hot end).

Obviously you can play with the numbers (upper and lower temperature bound, albedo) to get different answers (the big assumption was to just use the equilibrium temperature, but an atmosphere could warm things up a bit), but you should be able to follow this prescription using whatever numbers you wish.

Incidentally, at the "cool end" of the Mars calculation - the Earth's equilibrium temperature would be 315K (42 Celsius).