  The bad metallic phase with resistivity above the Mott-Ioffe-Regel limit,
which appears also in cuprate superconductors, was recently understood by cold
atom and computer simulations of the Hubbard model via charge susceptibility
and charge diffusion constant. However, since reliable simulations can be
typically done only at temperatures above the experimental temperatures, the
question for cuprate superconductors is still open. This paper addresses this
question by resorting to heat transport, which allows for the estimate of
electronic diffusion and it further combines it with the resistivity to
estimate the charge susceptibility. The doping and temperature dependencies of
diffusion constant and charge susceptibilities are shown and discussed for two
samples of YBa$_2$Cu$_3$O$_{6+x}$. Results indicate strongly incoherent
transport, mean free path corresponding to the Mott-Ioffe-Regel limit for the
underdoped sample at temperatures above ~200 K and significant effect of the
charge susceptibility on the resistivity.
