Would I be right in thinking then that for a non-aspirated probe on the ground, the temperature indicated is pretty inaccurate when probe heat is on?
You would be right
On that large Boeing which Spanner mentioned, if you have the Left Wing Bleed Duct depressurised(depriving the TAT probes of aspiration), the TAT will show high if the sun is shining directly on the probe (this is even before you have probe heat on). The probe heat test sends the TAT into orbit