  We consider the role of thermal diffusion due to turbulence and radiation on
accretion bursts that occur in protoplanetary discs which contain dead zones.
Using 1D viscous disc models we show that diffusive radial transport of heat is
important during the gravo-magnetic limit cycle, and can strongly modify the
duration and frequency of accretion outbursts. When the Prandtl number is large
- such that turbulent diffusion of heat is unimportant - radial radiative
diffusion reduces the burst duration compared to models with no diffusive
transport of heat. When the Prandtl number is small ($\lesssim 25$) we find
that turbulent diffusion dominates the radial transport of heat, reducing the
burst duration to $\lesssim 10^3$ years as well as increasing the burst
frequency. Furthermore, inclusion of radial transport of heat extends the range
of infall rates under which the disc undergoes accretion bursts from $10^{-8}$
to $10^{-6}$ M$_\odot$ yr$^{-1}$ with no diffusion, to $10^{-8}$ to
$\gtrsim10^{-4}$ M$_\odot$ yr$^{-1}$ with radiative and strong turbulent
diffusion. The relative roles of radiative and turbulent thermal diffusion are
likely to vary during an accretion burst, but simple estimates suggest that the
expected Prandtl numbers are of the order of 10 in protoplanetary discs, and
hence that turbulent diffusion is likely to be an important process during
accretion outbursts due to the gravo-magnetic limit cycle.
