The science
A thin accretion disc radiates the gravitational energy released as gas spirals inward. With a zero-torque inner edge at the innermost stable circular orbit (ISCO) the local effective temperature is
T(r) = [ 3 G M Mdot / (8 pi sigma r^3) * (1 - sqrt(r_in / r)) ]^(1/4)
so far from the hole T falls as r^(-3/4) and it peaks at r = (49/36) r_in. The ISCO of a spinning (Kerr) black hole follows Bardeen, Press and Teukolsky (1972): r_isco = 3 + Z2 - sqrt((3 - Z1)(3 + Z1 + 2 Z2)) with Z1 = 1 + (1-a^2)^(1/3) [(1+a)^(1/3) + (1-a)^(1/3)], Z2 = sqrt(3a^2 + Z1^2), in units of r_g = GM/c^2. The efficiency is 1 - E_isco.
Honest simplifications: the temperature law is the Newtonian Shakura-Sunyaev form evaluated at the Kerr ISCO. It leaves out relativistic corrections (Novikov-Thorne), colour hardening, Doppler beaming and light bending, so absolute temperatures near the hole are only indicative. The colour bar maps temperature to a blackbody colour and saturates at 40,000 K, because the true peak lies in the X-ray band. The radial scale of the picture is logarithmic.
Checks: ISCO from the closed form versus the numerical minimum of the specific angular momentum L(r); the T_max location 49/36 r_in; the r^(-3/4) slope; and the total luminosity integral versus GM Mdot / (2 r_in).