  Dust plays a key role in the formation of planets and its emission also
provides one of our most accessible views of protoplanetary discs. If set by
radiative equilibrium with the central star, the temperature of dust in the
disc plateaus at around $10-20$K in the outer regions. However sufficiently
nearby massive stars can heat the outer disc to substantially higher
temperatures. In this paper we study the radiative equilibrium temperature of
discs in the presence of massive external sources and gauge the effect that it
has on millimetre dust mass estimates. Since millimetre grains are not
entrained in any wind we focus on geometrically simple 2D-axisymmetric disc
models using radiative transfer calculations with both the host star and an
external source. Recent surveys have searched for evidence of massive stars
influencing disc evolution using disc properties as a function of projected
separation. In assuming a disc temperature of $20$K for a disc a distance $D$
from a strong radiation source, disc masses are overestimated by a factor that
scales with $D^{-1/2}$ interior to the separation that external heating becomes
important. This could significantly alter dust mass estimates of discs in close
proximity to $\theta^1$C in the Orion Nebular Cluster. We also make an initial
assessment of the effect upon snow lines. Within a parsec of an O star like
$\theta^1$C a CO snow line no longer exists, though the water snow line is
virtually unaffected except for very close separations of $\leq0.01\,$pc.
