We studied the accretion disc structure in the doubly imaged lensed quasar SDSS J1339+1310 using r-band light curves and UV-visible to near-IR spectra from the first 11 observational seasons after its discovery. The 2009-2019 light curves displayed pronounced microlensing variations on different timescales, and this microlensing signal permitted us to constrain the half-light radius of the 1930{AA} continuum-emitting region. Assuming an accretion disc with an axis inclined at 60{deg} to the line of sight, we obtained log(r_1/2_/cm)=15.4_-0.4+^+0.93%. We also estimated the central black hole mass from spectroscopic data. The width of the CIV, MgII, and H{beta} emission lines, and the continuum luminosity at 1350, 3000, and 5100{AA}, led to log(M_BH_/M_{sun}_)=8.6+/-0.4. Thus, hot gas responsible for the 1930{AA} continuum emission is likely orbiting a 4.0x10^8^M_{sun}_ black hole at an r_1/2_ of only a few tens of Schwarzschild radii.