Most power transformers operating in a power system possess oil-paper insulation. A serious defect of this type of insulation, which is associated with long operation time, is an increase in the moisture content. Moisture introduces a number of threats to proper operation of the transformer, e.g., ignition of partial discharges (PDs). Due to the varying temperature of the insulation system during the unit's normal operation, a dynamic change (migration of water) takes place, precipitating the oil-paper system from a state of hydrodynamic equilibrium. This causes the PDs to be variable in time, and they may intensify or extinguish. Studies on model objects have been conducted to determine the conditions (temperature, humidity, time) that will have an impact on the ignition and intensity of the observed phenomenon of PDs. The conclusions of this study will have a practical application in the evaluation of measurements conducted in the field, especially in relation to the registration of an online PD monitoring system.