Not a meteorologist, but from my understanding that would be quite unlikely[1]. Furthermore, it seems odd that warmer temperatures in the area they are migrating
to would trigger an early arrival (how would they know?). A more plausible hypothesis might be abnormally cool summer/early fall in the southern hemisphere, or other conditions local to the swallows southern nesting sites.
[1]: https://en.m.wikipedia.org/wiki/Little_Ice_Age