True, the first thing to look into with the sweating, is the possibility you are over medicated. But the way to check that, is to run TSH, FT4 and FT3. It doesn't sound as if you are familiar with those values.
If you are truly over medicated, and apparently your Doctor thinks you are, then the course of action would be to lower your dose, and/or, if warranted, to change the mix of meds, based on the relationship of FT4 to FT3.
The question is, are you over medicated?
Well that depends on what was "up to 3.something".
If your TSH was 3.something, then it is possible you were under medicated. If this is the case, then it makes sense to look into other possibilities. As the previous poster mentioned, she had sweats with Synthroid. Of all the thyroid medications, the one I hear more people having adverse reactions to (outside of being over medicated), is Synthroid. Theories I have heard on this, seem to point to the non-active ingredients, rather than the active T4 itself. For that, and other reasons, you could try switching to one of the other T4 meds, such as Unithroid or Levoxyl.
If it was your Free T3 that was 3. something, then it depends on what the .something was. 3.0 for some people means under medicated. 3.5 might be about right. 3.9, might be a bit much for many people.
I would call the Doctor's office, and ask the office clerks to fax you a copy of your latest test results, and post them here for opinions.