The problem with the transistor you are describing is common for the problem at hand. The need for this large 250W resistor is related to the current flowing through it. Replacing the resistor with e.g. a transistor will produce the same amount of heat as the resistor.
If you want to use the same technique as the resistor, you need to cool it. A small circuit diagram would be very helpfull for me to solve the problem. As I understand it, you want to slow down a DC-motor by lowering the voltage across it. What I don't understand is the voltages and resistances. It seems that your powersupply can not handle the load and droppes in voltage.
If this is your goal, then there is an other solution. You could use a Solid State Relay for speed regulation.
http://pcbheaven.com/scripts/imageprese ... 790375.jpgThis is just an example how to look at it.
The basic principle is P=UxI (Power (heat produced) = U (Voltage across the load that produces the heat) x I (Current flowing throug this load).
If the current is Zero, the heat is zero. If the voltage across the load (The resistor of transistor) is zero, also the heat produced is zero. Only if you are in those between, the power, thus the heat increses.
In your example it would be 93V x 0.80 A = 74.4 Watt. Or, 93 x 2.21 = 205,53 W (but this would be the power consumed by the DC-Motor i presume).
Hope to have pointed you in the right direction.
Please excuse my English, I'm from the Netherlands and it's a bit rusty

Greets,
Wim