It is generally considered that a non-Jew cannot be invited to a hot meal on Yom-Tov because it is a melacha to heat up food for them (from what I've heard, even if it is as part of a group including Jews and there is plenty of food). Is anyone aware of any heterim for this? (eg. for inviting people in the process of conversion)
In siman 512 the allowance given by the Mechaber is to cook for one's servant maid etc or a no-Jew who comes himself.
Mishna Berurah explains that the only time we have the concern of coming to cook specifically for a non-Jew is when they were important enough to invite. In that case we are afraid one may accidentally come to cook specifically for them which is a biblical prohibition.
Ramma adds that when cooking for himself, he can actually add extra food for the non-jew. This is only written about the non-Jew the Mechaber was talking about, a servant or maid. However this allowance does not extend to other non-jews. From the Aruch HaShulchan siff 6 it appears a person who shows up by himself would be included in the prohibited group.
Also in the Aruch HaShulchan siff 5 he brings another hetter to invite a non-Jew as long as the food was already cooked. The Aruch HaShulchan though goes on to explain that the situation cannot be that one had intended to invite him from before he started cooking. It would be impossible to say he didn't have this guest in mind when cooking. He says this only works if one cooked the food, and then bumped into this non-Jew close to meal time, and invited him to the completely ready meal.
One clarification though, you mention heating up food in your question. I would doubt heating up food that was previously cooked is included in this Rabbinic enactment. But clear that up with your religious authority.