Following the successful pressure loading with DT of a thin-walled plastic inertial fusion target shell (such as those designed for use at the OMEGA facility at the University of Rochester's Laboratory for Laser Energetics (UR/LLE)), continual care must be taken to safeguard the shell from being exposed to unacceptable pressure differentials across its wall. In particular, once the DT has been condensed into a liquid or solid phase and the outside pressure has been reduced, the target must be maintained below some upper cutoff temperature such that the vapor pressure of the DT is below the bursting pressure for the shell. Through the process of β-decay the DT self-heats, but while the shell is in a high vacuum environment (P << 0.8 Pa (6 mtorr) for the OMEGA layering sphere) there is only a negligible heat loss mechanism. This will cause the temperature to increase. A calculation has been done to estimate the rate of temperature increase of the loaded target under high vacuum conditions. A functional form for calculating the target's temperature increase given its starting temperature is presented. An overall result is that under high vacuum conditions the DT changes from a solid at 10 K to a liquid at 37 K (Tc=39.4 K) in about 19 minutes. This “holding time” is significantly less if the initial temperature is higher, the initial state is liquid, or the upper allowed temperature is lower. Simplifying assumptions which were made and their impact on interpreting the results of this calculation are discussed.