Cooling wort

I am a noob at this so please don't hold it against me if this question seems stupid. Just brewed an Oktoberfest lager and had to rapidly chill it down to 60 degrees before transfering to primary. Is it OK to ocasionally stir up the wort during this phase to get a more accurate reading on the temp? I am worried about bringing up all the trube and unwanted proteins, instead of letting it settle down, but there seems to be very different levels of temp throughout the wort when I move the thermometer. In the end I did stir it up a bit. In this case would you use a filter or strainer to keep the trube from going into the primary when transferring? any help with this phase would be appreciated

Stir all you want. After it's cool you can let it rest for 20 min or so and all the trub will drop to the bottom.

But really I don't think it's a big deal if you get some trub in your fermenter. RDWHAHB

Stirring is ok, and getting hop remnants and coldbreak in the fermenter isn't a problem either. The biggest thing to watch out for is once it's below 140 or so, you increase the risk of infection.

I stir the cooling wort to get faster cooling, not better temp readings. I would (and do) whirlpool that before siphoning off the side of the boil kettle. From what I understand, whirlpooling is pretty standard practice.

Amanda