Well, we understand stellar physics pretty well, so unless you're going to invent some new physics (which might as well be magic) the only answer seems to be to find a way to add matter to the Sun. (For a main sequence star, the temperature and luminosity increases with increasing mass. The Sun is a main sequence star, and if it left the main sequence, the consequences for Earth would be much worse than just some hotter weather. So the Sun needs to remain on the main sequence.)
I can see three ways to get added mass -- or, rather, three kinds of added mass: Normal matter, dark matter, black holes. Note that the amount of added matter needed is large -- multiple Jupiter masses, or tens of thousands of Earth masses. All the planets in the Solar System are probably not enough.
Getting more normal matter into the Sun is not impossible, but is pretty hard to do without adversely impacting (pun intended) the Earth. Basically, you need a reason that vast quantities of solid matter -- comets, planets, whatever, come streaming into the Sun more or less perpendicular to the ecliptic. (This is so that you don't have to have the incoming debris dodge the Earth -- or the Earth to dodge the incoming debris.) The problem is that we have absolutely no reason to think that such masses of matter exist or that it would stream straight into the Sun.
(It's easier to imagine that there's a lot of cold matter -- a super-dense Oort Cloud -- moving towards the Solar System. We can barely detect our own Kuipier Belt, and it's much closer and much denser that the Oort Cloud would be until just before it hits. The problem is that it would not stream towards the Sun, but would necessarily be much wider than the Solar System and would hit all the planets as well. It would appear to us as a huge flood of comets all coming from the same direction -- a bit like driving into a snow storm where the snowflakes are comets. To get enough matter into the Sun that way would pummel the Earth.)
I think Dark Matter is your answer. DM doesn't interact with normal matter except gravitationally, and it's very hard to detect. While we have no reason to think that local concentrations exist (and some good theoretical ones to think they don't) we can not presently not tell from observation one way or the other. Finally, while we think that DM doesn't interact much with normal matter, we could be wrong. Postulate that when NM is hot enough and dense enough there's a frictional interaction with DM.
So postulate that the Solar System plows into a really, really dense clump of DM. The Earth flies right through it with no more than a few blips on scientists' instruments, but the center of the Sun being hot and dense picks up a huge mass of it. The DM doesn't participate in fusion, but it does make the Sun more massive and the added pressure raises energy production and thus luminosity. It might work.
Black Holes maybe might work. What you need, I think, is for the Sun to encounter a swarm of Jupiter-mass (or perhaps smaller) BHs, once again aimed right at the Sun from outside the ecliptic. (Aimed? By whom?) They should be small enough that they don't immediately swallow the Sun, but would be massive enough to increase the Sun's mass and hence luminosity.
The problem with the BHs is that they eventually would eat the Sun. Oops.
The problem with all these schemes is that it takes ca. a million years for an increase in fusion in the Sun's core to work its way out to the surface and increase luminosity. So (a) this means that the increased mass must have arrived a million years ago and (b) it also means that we would not see a sudden (only 500 years!) increase, but a gradual increase lasting a hundred thousand years or more.
So some rapid talking and handwaving will be necessary regardless.