  The precise estimation of small parameters is a challenging problem in
quantum metrology. Here, we introduce a protocol for accurately measuring weak
magnetic fields using a two-level magnetometer, which is coupled to two (hot
and cold) thermal baths and operated as a two-stroke quantum thermal machine.
Its working substance consists of a two-level system (TLS), generated by an
unknown weak magnetic field acting on a qubit, and a second TLS arising due to
the application of a known strong and tunable field on another qubit. Depending
on this field, the machine may either act as an engine or a refrigerator. Under
feasible conditions, determining this transition point allows to reduce the
relative error of the measurement of the weak unknown magnetic field by the
ratio of the temperatures of the colder bath to the hotter bath.
