  Measurements of the Hubble constant to distant galaxy clusters using the
Sunyaev-Zeldovich effect are systematically low in comparison to values
obtained by other means. These measurements usually assume a spherical
isothermal $\beta$ model for the intracluster medium (ICM). We present the
results of a statistical analysis of {\em temperature bias} in $H_0$
determinations in a sample of 27 numerically simulated X-ray clusters drawn
from a $\Lambda$CDM model at z=0.5. We employ adaptive mesh refinement to
provide high resolution (15.6 h$^{-1} kpc$) in cluster cores which dominate the
X-ray and radio signals. Fitting synthetic X-ray and y-parameter maps to the
standard isothermal beta model, we find a broad, skewed distribution in
$f\equiv H_0(SZ)/H_0(actual)$ with a mean, median, and standard deviation of
0.89, 0.83 and 0.32 respectively, where $H_0(SZ)$ is the value of $H_0$ derived
by using Sunyaev-Zeldovich effect method and $H_0(actual)$ is the value used in
the cosmological simulation. We find that the clusters' declining temperature
profiles systematically lower estimates of $H_0$ by 10% to 20%. The declining
temperature profile of our adiabatic system is consistent with the result
including radiative cooling and supernovae feedback (Loken et al. 2002). We
thereby introduce a non-isothermal $\beta$ model as an improvement. Applying
the non-isothermal $\beta$ model to the refined sample with well-fitted
temperature profile, the value of f improves 9% relative to the actual value.
The study of the morphology and the clumping effects conclude that these two
factors combine to induce scatter in f of $\pm$ 30 %.
