#1: Wasn't too sweaty upon arrival (wore workout clothes, early morning chill helped)
In winter, I wear my office clothes, and I only occasionally need to dry off from overdressing. In summer, I wear my office pants with a T-shirt and change my shirt at work. The hotter it is, the less I push myself. I don't take a shower at work, but my commute is only 2 miles.
#2: Acquired backpack (hand-me-down, free)
Wearing a backpack has three negatives:
1) It puts a bigger load on your body, which over time can cause back and butt pain.
2) It restricts airflow to your back, so your back gets sweaty.
3) It raises your center of mass, which might affect handling during aggressive maneuvers.
See if you can get a rear rack or otherwise safely mount a bag to your bike (e.g., doesn't contact your spokes). I have a Planet Bike Eco Rack and a Racktime BuyIt Pannier. There are Instructables for making your own, too, including several for how to turn a backpack into a pannier.