To explain the activity of active galactic nuclei or compact X-ray sources, I consider a black hole magnetosphere in the center of these objects. The considering black hole magnetosphere is composed of a massive black hole with surrounding fluids and magnetic fields, and rotates rapidly. Because of the strong gravitation and the rapid rotation, both an accretion and a wind/jet would be generated from plasma sources (e.g., an accretion disk and its corona). The outgoing flow carries the angular momentum from the plasma source effectively, and then the accretion would go on stationary, releasing its gravitational energy. I assume that the magnetosphere is stationary and axisymmetric, and that the ideal MHD approximation is available for the streaming fluid. I discuss the thermal effects on MHD flows, and then I argue that the trans-fast MHD accretion solution can be broken by highly thermal effects.