Will using an SSR on the secondary side of a transformer lead to heating due to harmonics?
The SSR generates current harmonics, which in a single phase system will only disturb the power factor slightly. It's only in a 3 phase system that such harmonics do other bad things like exciting neutral currents.

While a reduced power factor means there will be more heating in your secondary (and primary) for the same heater power than would be caused by a unity power factor, the effect with an SSR is going to be negligible.