so, would you run this inside your tent?

I have the exact same heater. I used on sevral cold winter camping trips and have had no problems with it or waking up.

Just to add: Used this model last September in a 10x10 canvas tent on our Grand Canyon/Colorado/New Mexico trip . Only used it at night to warn the tent up and in the morning to warm it up for the wife. She was happy, I was happy! We used nice toasty sleeping bags during the night. One propane bottle lasted about a week. I keep it as a backup for winter time power outages... very useful...