  Context. FU Orionis is the archetypal FUor star, a subclass of young stellar
object (YSO) that undergo rapid brightening events, often gaining 4-6
magnitudes on timescales of days. This brightening is often associated with a
massive increase in accretion; one of the most ubiquitous processes in
astrophysics from planets and stars to super-massive black holes. We present
multi-band interferometric observations of the FU Ori circumstellar
environment, including the first J-band interferometric observations of a YSO.
Aims. We investigate the morphology and temperature gradient of the inner-most
regions of the accretion disk around FU Orionis. We aim to characterise the
heating mechanisms of the disk and comment on potential outburst triggering
processes. Methods. Recent upgrades to the MIRC-X instrument at the CHARA array
allowed the first dual-band J and H observations of YSOs.Using baselines up to
331 m, we present high angular resolution data of a YSO covering the
near-infrared bands J, H, and K. The unprecedented spectral range of the data
allows us to apply temperature gradient models to the innermost regions of FU
Ori. Results. We spatially resolve the innermost astronomical unit of the disk
and determine the exponent of the temperature gradient of the inner disk to
$T=r^{-0.74\pm0.02}$. This agrees with theoretical work that predicts $T =
r^{-0.75}$ for actively accreting, steady state disks, a value only obtainable
through viscous heating within the disk. We find a disk which extends down to
the stellar surface at $0.015\pm0.007$ au where the temperature is found to be
$5800\pm700$ K indicating boundary layer accretion. We find a disk inclined at
$32\pm4^\circ$ with a minor-axis position angle of $34\pm11^\circ$.
