I have a GE Profile side by side refrigerator. It has not been cooling very well, it stays between 38-41 degrees. also the ice maker doesn't make a lot of ice and the cubes are smaller in size.

SOURCE: GE 25 side by side refrigerator ice maker problem

Assuming the temp inside the freezer is at around 0 or -2 degrees, it should dump ice every ~50 minutes or so. Again, depending on temp's, an Ice Bin should fill within 24 to 48 hours. If your freezer temp is running at around 10 degrees, everything will obviously still be frozen (below 32), but the ice maker will take longer to freeze the water than it would if it were at 0 degrees. Open both doors and place the palm of your hand on the partition between the freezer and Fresh Food compartments... (where the door gaskets seat when they're closed). The temp of the partition should be about 5 or 10 degrees warmer than body temp., If it's hotter than that, you found the problem. Either the condenser coils are dirty and need a good cleaning OR your condenser fan motor (the fan in back, near the floor in the compressor area) is failed or about to fail.

SOURCE: Whirlpool side-by-side refrigerator ice dispenser

First pull out the ice bucket and close the door.  Set for cubed ice.  Press the button for ice to come out and listen for a loud clunk noise.  That is the sound of the solenoid.  You can open the door, hold the light switch and press the button and watch for the solenoid moving up and down.  Solenoid is at the back of the freezer in a little square opening where the rod on the ice bucket goes into.  If that solenoid is moving ok then put the bucket back in while the solenoid is in the down position and cubes should work.  If solenoid is not working then it will need to be replaced.  Let me know what you find.

SOURCE: Ge profile side By side ice maker water leak

This sounds like the float mechanism has gone bad. Remove it and have a look. It may be the float or the switch on it that is bad. There is also a solenoid valve. Parts kits are available. Shut off the water first!

SOURCE: GE top freezer ice maker leak

I have the same problem -

SOURCE: GE Profile refrigerator ice maker stopped working

I had the same problem where one of the solinoids in the valve- the one controlling water to the ice machine had stopped working. A good test is to pour water into where the ice cubes are made. If ice cubes come out then the problem is most likely in the valve. I replaced my valve for the second time in 8 years today and the ice is comming out nicely.