Within a combined experimental and theoretical study it is shown that the spin Hall angle of a substitutional alloy system can be continuously varied via its composition. For the alloy system Au_{x}Pt_{1-x} a substantial increase of the maximum spin Hall angle compared to the pure alloy partners could be achieved this way. The experimental findings for the longitudinal charge conductivity σ, the transverse spin Hall conductivity σ_{SH}, and the spin Hall angle α_{SH} could be confirmed by calculations based on Kubo's linear response formalism. Calculations of these response quantities for different temperatures show that the divergent behavior of σ and σ_{SH} is rapidly suppressed with increasing temperature. As a consequence, σ_{SH} is dominated at higher temperatures by its intrinsic contribution that has only a rather weak temperature dependence.