"Discharge" of what??
If it is Lightning Discharge, the resistors are always non-linear - resistance of the resistor stack falling rapidly once the rated voltage threshold is crossed.
If it's a synchronous machine (generator or motor) with brushless excitation, that "discharge resistor" may be the method of limiting damage to the rotor windings in event of a stator (short circuit) fault. If that is the case, the resistance is (usually) linear over the expected operating temperature range of the resistor - which may be dramatically different from the machine "nameplate" temperature rise, by the way.
For the brushless excitation, the resistor is typically the same kind as that used to prevent condensation in air handling environments. The device is typically not finned (although it could be) and is a circuit comprised of several "strip" or "tube" type resistive elements connected in some series/parallel combination.
Gr8blu, You could be right that the O means Discharge resistor in generator field circuit.
Discharge resistor in generator field circuit is cut in whenever Field Contactor is open.
This is to short circuit the Generator field winding so that the stored energy in the field windings is quickly discharged.
