My two cents in no particular order:

Aside from the big seat bags that Tarwheel shows you can simply roll up a bundle and bungie it in the same place behind the seat. In practice that's a little inconvenient but works in a pinch. You can also purchase or DIY a frame bag that hangs in the front triangle. I did this, and it works very well if you fashion it for quick attachment and release. It won't be big enough for the work boots so you have to work something else out for that (can you leave them at work?). I'd consider a seatpost rack just for the shoes.

You should get a frame pump or tiny CO2 pump. That's the one thing that I don't consider optional, along with patches and/or tubes. I carry all of the above, all of the time.

Just leave the lock at work. There's no reason to carry it around if you go to the same place every day.

Biking shorts, chamois padding et al are entirely optional for a 10 mile commute.

Don't worry about going the 10 miles in 85°, you can adapt easily and it will eventually become routine. I don't even bother with water for that distance, in sometimes considerably warmer temperatures in our summers. Just get on your bike and ride, take a backpack if you have to - it's not that bad.