When is the car "warmed up" enough to not drive like a granny?
 

The majority of my trips are only 5 to 15 miles, so I'm wondering what temperature is "safe" for hitting the acceleration a bit more aggressively.

Currently, I run the car for at least 30 seconds to a minute before I put it into drive. I try to "granny" it until it reaches 180 to 200 degrees, and I won't floor it unless it's close to 220 (usually, this means I'm on a extended canyon cruise, as it usually takes a while for it to get this hot).

Are these numbers about right?

I think you can put the hammer down by 180F. I typically try to stay below 3k RPM until my oil temps are 'reading' and the needle is off the bottom and starting to climb. Then I keep it below 4k RPM until I'm at 180F.

I go at 180, too.

Same ^^