Hyundai Repair: 2002 Sonata wont start when very cold out., starter solenoid, battery cables

Question
However, when it warms up a little the car *tries* to turn over and then eventually succeeds. It starts very slow.

I've replaced the battery and the battery cables. I read somewhere that it might be the solenoid or the starter.

Since it starts when warmer, I think it's the solenoid.

Will auto shops replace just a solenoid? How much does this cost?

Would it be possible to do it myself? If so, is there a link somewhere that details the steps in changing the solenoid?

Thanks.

Answer
The starter solenoid is part of the starter and cannot be replaced separately.  

Based on your description, it sounds like your system voltage is low, you have a voltage drop in the cables, or the starter motor is dragging while it turns.  I know you've changed the battery and cables, but starter problems on Hyundai are very, very rare.  

If you have a voltmeter, check the battery voltage while cranking.  Then clip the positive lead on the starter lug and the negative lead onto the starter body.  Again check the voltage while cranking.  Your readings should be similar and above 10V.  Readings below 10V indicate a low battery state of charge.  Readings significantly different from one another indicate a problem with the battery cables.