A standard Shakura & Sunyaev (1973) thin accretion disk radiates as a local blackbody at every radius, with an effective temperature profile that falls off steeply with distance from the inner edge:
T(r) = T_in · (r_in/r)^0.75 · [1 - √(r_in/r)]^0.25
The r-0.75 power law is the reason a real accretion disk shows a sharp color gradient: the innermost annuli — sheared fastest by differential (Keplerian) rotation — dissipate far more heat per unit area than the slow-moving outer disk, so the disk runs from blinding blue-white/UV near the inner edge to dull deep red at the rim. The bracketed term forces T → 0 exactly at the inner edge itself (the torque-free boundary condition), which is why the very brightest ring sits just outside r_in rather than on top of it.
The characteristic inner-edge temperature itself scales with how much matter is falling in and how deep the potential well is:
T_in ∝ (Ṁ · M)^0.25
Raising the accretion-rate slider Ṁ dumps more gravitational energy into the disk per second; raising the central-mass slider M deepens the well feeding that energy release. Either one shifts the entire temperature profile up together — the shape (r-0.75) never changes, only its overall scale — which is why real X-ray binaries (stellar-mass black holes, high Ṁ) run millions of degrees hotter than the disks around supermassive black holes even though both obey the exact same power law. The rendered ring on the left maps T(r) at every radius through a real blackbody color-temperature approximation; the graph on the right plots the same T(r) curve directly against radius.