Runs fine until it warms up then it acts like the chain brake is on and won't run

I am going to close this, you can continue to reply and I will continue respond to the best of my ability.
Actually the slipping clutch is a good likelihood. I might lean toward an abraded clutch face. I will post what I consider a pretty good removal method. A couple of other things that come to mind from your description are:
1. When it begins to give you trouble, check the oiler operation. If the chain and bar get hot they will bind.
2. Do the same with the sprocket nose. You should not need to remove the bar, loosen it, slide the bar tight against the drive sprocket, loosen the chain at the nose of the bar and ensure you can easily rotate the sprocket in the nose of the bar. I do not think it #2 but it is a possibility.

Your basic model number is 600035. There are 11-, 21-, and 22- prefixes used with 600035s. There are also a ton of suffixes with the 600035s. I think the suffix is on your saw immediately after the basic model number somewhere (usually on bottom of older Macs along with the serial number. The dash of the serial on older Macs is the prefix). I must defer to you to find your exact IPL, here:
McCulloch IPLs
http://www.ordertree.com/modelinfo/McCulloch/139.59.html

I chose this one as an example "22-600035-58" for an IPL
http://www.ordertree.com/modelinfo/MCC/22-600035-58-Mac-3516-IPL-211229-01/139.22-600035-58-Mac-3516-IPL-211229-01.1.59.1.html
I find these helpful when getting into an area of repair I am unfamiliar with. Also clutch parts are displayed and part numbers listed.

She has an outboard clutch and this is very help with removal:
R² Drive Link Outboard Clutch by Drivelink.blogspot.com
http://www.youtube.com/watch?v=cdqkIuVNUQc

1. Check the IPL for your saw to see if any special tools are needed. Poulan (Craftsman, Jonsered, Husky) clutch removal tool part number 530031112 if needed, is under $5 from many sources (look at the visible area between the weights if 2 small round sockets are visible you need the tool).
2. There are metal piston stops available, when square (almost never) with the piston top these work well, if not square they have been known to punch through the piston. I suggest a length of nylon rope (nothing left behind) be used instead of the piston stop (retain 6" ± so you can remove it). Make sure the piston is near the top of the cylinder before feeding the cord or it can fall through the exhaust port and damage the piston as it rises.
3. Everyone I have ever removed had a left handed thread (tighten it to loosen it).