Ultracold electron sources, which are based on near-threshold photo- and field-ionization of a cloud of laser-cooled atoms, offer the unique combination of low emittance and extended size that is essential for achieving single-shot, ultrafast electron diffraction of macromolecules. Here we present measurements of the effective temperature of such a pulsed electron source employing rubidium atoms that are magneto-optically trapped at the center of an accelerator structure. Transverse source temperatures ranging from 200 K down to 10 K are demonstrated, controllable with the wavelength of the ionization laser. Together with the 50 μm source size, the achievable temperature enables a transverse coherence length of ≈20 nm for a 100 μm sample size.