  While the ability to measure low temperatures accurately in quantum systems
is important in a wide range of experiments, the possibilities and the
fundamental limits of quantum thermometry are not yet fully understood
theoretically. Here we develop a general approach to low-temperature quantum
thermometry, taking into account restrictions arising not only from the sample
but also from the measurement process. We derive a fundamental bound on the
minimal uncertainty for any temperature measurement that has a finite
resolution. A similar bound can be obtained from the third law of
thermodynamics. Moreover, we identify a mechanism enabling sub-exponential
scaling, even in the regime of finite resolution. We illustrate this effect in
the case of thermometry on a fermionic tight-binding chain with access to only
two lattice sites, where we find a quadratic divergence of the uncertainty. We
also give illustrative examples of ideal quantum gases and a square-lattice
Ising model, highlighting the role of phase transitions.
