  A milestone of modern cosmology was the prediction and serendipitous
discovery of the Cosmic Microwave Background (CMB), the radiation left over
after decoupling from matter in the early evolutionary stages of the Universe.
A prediction of the standard hot Big-Bang model is the linear increase with
redshift of the black-body temperature of the CMB (TCMB). This radiation
excites the rotational levels of some interstellar molecules, including carbon
monoxide (CO), which can serve as cosmic thermometers. Using three new and two
previously reported CO absorption-line systems detected in quasar spectra
during a systematic survey carried out using VLT/UVES, we constrain the
evolution of TCMB to z~3. Combining our precise measurements with previous
constraints, we obtain TCMB(z)=(2.725+/-0.002)x(1+z)^(1-beta) K with
beta=-0.007+/-0.027, a more than two-fold improvement in precision. The
measurements are consistent with the standard (i.e. adiabatic, beta=0) Big-Bang
model and provide a strong constraint on the effective equation of state of
decaying dark energy (i.e. w_eff=-0.996+/-0.025).
