The unique compact radio source, Sgr $A^*$, at the Galactic center show many observational signs that it is powered by supermassive black hole. Recent observations also imply that it is surrounded by winds from nearby IR sources. So we explore the model in which multiwavelength spectrum from Sgr $A^*$ is due to the spherical accretion of these winds onto the central supermassive black hole. Improving upon the previous work, we allowed the possibility that ions and electrons have different temperatures, included the Compton effects and pair processes. Electrons radiate via cyclosynchrotron and bresstrahlung with comptoniztion. We find that ion approaches the virial temperature ${\sim}10^{13}K$ while electron temperature saturates at ${\sim}10^{10}K$. However, decoupling between ion and electron does not greatly affect the shape of the emission spectrum. When the mass of the black hole is ${\sim}10^6M_{\odot}$, radio, IR, X-ray, $\gamma$-ray band spectrum is reasonably explained by the model. Yet Compton effect which is neglected in previous works produces significant emission in IR band, which is marginally compatible with observations. Pair production is negligible and annihilation lines cannot be observed.