Hello, I'll be 40 soon

and my daughters surprised me with the one thing I've wanted for as long as I can remember.... a snake!
So, our newest family member is a corn snake!
We have him in a plastic box, sold by the retailer, with a heatpad under one end, some substrate, waterbowl, some special wood blocks (we've creatively made a cave out of!)
He's about 12" long. He seems very fit & well. Active and bright eyed.
But two things concern me, 1. We didn't get a thermometer thingy to stick on the box, and 2. The heat pad doesn't seem to warm enough, should I put it against the side (it says you can do so on the heat pad info). Where snake is situated is on my desk, and we have an poiseangle lamp ~ can I direct that close to it to add heat during the day?
Any advice gladly taken. I've been reading books & looking at websites all afternoon, and I'm more confused now then ever ~ and these are meant to be the easiest to keep!
TYIA x