Why does the potentiometer burn up in my setup?
If the pot is rated at 1 watt (end to end of course) it will be rated at 0.1 watts for 10 % of its travel (100 ohms) or 0.01 watts at 1% of its travel (10 ohms).

So, say you have the wiper positioned to provide 10 ohms and this is feeding a stalled motor from a 12 volt supply, there might be up to 1 amp trying to flow thru the 10 ohm part of the pot.

This is a power dissipation (in that 10 ohm part of your pot) of 10 watts and if the pot was only generally rated at 1 watt (end-to-end) it will fry (in an instant) over that small section of the pot that was producing 10 ohms between wiper and one end.

Think about it another way - it's a 1k pot and say it's rated at a sizable 10 watts - power = current-squared multiplied by resistance - so : -

10 watts = \$I^2\times 1000\$ or \$I^2 = 0.01\$ or \$I = 100mA\$

Any current greater than 100mA thru a 1k 10 watt pot will exceed its rating. If it's a 1 watt pot then any current thru the 1k pot greater than 31.6 mA is exceeding its rating.