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.
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