i would replace the thermostat first, just doing that may release any air bottled up in there if there is any. if you do do it try to park the car so the front is up as high as possible. help any air out thats stubborn. sticky/stuck thermostat or one that only opens part way would do what your seeing. how dirty was the system? any clumps of stuff come out?

 

When I flushed it, there was a lot of sludge.

 

Seriously, nobody caught this?
Half way on the gauge is 210 degrees.
Your engine is NOT "overheating"
What the gauge is reading at idle (and going a little higher) is perfectly normal.
Your fan isn't set to go on till the engine hits a little over 220 degrees. Again, that's normal.
Perhaps the flush, after cleaning out the sludge, has "fixed" the incorrect low gauge reading you used to be getting.
Drive the car, there's nothing wrong here.

 

when you did the flush was there chuncks comin out or just fine material? yah look to see if the thermostat is gunked up and when you do have a look at any thing that comes out, may have something that got stuffed up in the block.