This is really more an issue of target stability than one of safety. However, a target with a carefully regulated temperature will presumably not undergo worrisome pressure changes.
Each target contains four quality temperature measurements, two Cernox resistors and two hydrogen vapor pressure thermometers. The primary temperature regulation is done with a dedicated temperature controller (an Oxford ITC-502) which slaves a heater (the "low power heater") to the temperature read by one of the Cernox resistors. This is a three parameter control loop (Proportional, Integral and Differential Control or PID).
In addition, the return temperature of the target systems coolant gas is used to regulate the supply of coolant from ESR.
Finally, the heat load from the beam will be compensated in the "active" target loop by use of the high power heater. This is not a true regulation but rather a one for one replacement of the beam load should the beam disappear for whatever reason. The beam load is calculated from the target length, the beam current as read from a current monitor and the target material.
Excursions of the target temperature outside acceptable limits will cause the control system to take action. Finally the redundancy of temperature measurements can be used by the control system to pick up the failure of a sensor or its readout channel. A more complete discussion of target temperature regulation is available in Reference [6].