  We explore the effects of frequent, impulsive quantum nondemolition
measurements of the energy of two-level systems (TLS), alias qubits, in contact
with a thermal bath. The resulting entropy and temperature of both the system
and the bath are found to be completely determined by the measurement rate, and
unrelated to what is expected by standard thermodynamical rules that hold for
Markovian baths. These anomalies allow for very fast control of heating,
cooling and state-purification (entropy reduction) of qubits, much sooner than
their thermal equilibration time.
