  The Belle II experiment currently under construction at the $e^+e^-$-collider
SuperKEKB in Japan is designed to explore new physics beyond the standard model
with an approximately 50 times larger data sample compared to its predecessor.
The vertex detector (VXD), comprising a two layer DEPFET pixel detector (PXD)
surrounded by four layers of double sided silicon strip detector (SVD), is
indispensable for the accurate determination of the decay point of $B$ or $D$
meson as well as track reconstruction of low momentum particles. The DEPFET
sensors in Belle II are thinned down to 75 $\mu$m with low power consumption
and low intrinsic noise. In the DEPFET concept, the front-end electronics is
placed outside of the sensitive area, and thus no cooling components are
necessary inside the physics acceptance of the detector. Evaporative two-phase
CO$_2$ cooling in combination with forced air flow has been chosen as the
scheme for the PXD cooling. To guarantee the DEPFET detector operation
condition and verify the cooling concept, a PXD mockup is constructed at DESY.
Studies of the thermal and mechanical performance are presented in this paper.
