  Cold atomic gases provide a remarkable testbed to study the physics of
interacting many-body quantum systems. They have started to play a major role
as quantum simulators, given the high degree of control that is possible. A
crucial element is given by the necessarily non-zero temperature. However
cooling to the required ultralow temperatures or even simply measuring the
temperature directly on the system can prove to be very challenging tasks.
Here, we implement thermometry on strongly interacting two- and one-dimensional
Bose gases with high sensitivity in the nano-Kelvin temperature range. Our
method is aided by the fact that the decay of the first-order correlation
function is very sensitive to the temperature when interactions are strong. We
find that there may be a significant temperature variation when the
three-dimensional quantum gas is cut into two-dimensional slices or into
one-dimensional tubes. Strikingly, the temperature for the one-dimensional case
can be much lower than the initial temperature. Our findings show that this
decrease results from the interplay of dimensional reduction and strong
interactions.
