In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. In this talk, I will first introduce an operational formulation of the third law as a constraint on the class of realisable channels, such that the availability of a channel not so constrained is both necessary and sufficient for the attainability of pure states. Subsequently, I will show how the third law thus construed limits measurements of general observables, or POVMs. In particular, it is shown that while the third law categorically precludes ideal or repeatable measurements, non-disturbing measurements can be achieved if the measured observable is sufficiently "unsharp".