This can be done by installing a close fitting bushing into the bottom of the stuffing box and using a recirculation line from the pump discharge to pressurize the box. As noted above, be careful of leaks in the fittings. This could be dangerous in some high pressure boiler feed pump or boiler circulating pump applications. Depending upon the pressures involved you may be better off with a special high pressure seal design. You are going to have trouble when the heat transfers back to the bearing oil.
Many pumps have a bearing oil cooler available to provide the necessary cooling.
Check with the manufacturer for this accessory. The lip or grease seals used in these applications have a useful life of only three months also, even when the temperature is closely controlled. These seals should be replaced with labyrinth or positive face seals. It is not wise to install a cooler between the pump discharge and a conventional stuffing box. Although this arrangement will provide adequate cooling, in most cases it is too dangerous at elevated temperatures because of possible leaks in the piping and fittings.