Yes there are. Scientists compare the measurements from both methods in the time when there's data from both. For example ice cores formed last decade should match direct temperature measurements from last decade. It's the same way the oldest rings from living trees are matched against the newest rings from tree fossils, and radiocarbon dating is checked against all of that.

That does not look very reliable to me, because that implies certain things are only affected by ambient temperature.

Btw, Can you tell me how ancient temperature is measured from ice cores? My lookup only says we can detect atmospheric composition, and not temperatures from the ice cores.