I recently saw a thread where someone baked cakes INSIDE Starbucks cups. Will that start a fire in my oven? How do I go about this the safest way possible?

Starbucks was gracious enough to GIVE me several cups today, and I'd really LOVE to try this out.

Thank you so much.. and YES, I'm a pyrophobic.

Wrap the cup in aluminum foil and it will be fine. Keep the temp at 300 or 325 - no higher.
I have not used those cups but often have used oatmeal box (round container) to bake gingerbread pieces by wrapping in foil.

Paper burns at 450 degrees.

I use paper all the time to cover turkeys, etc. Never caught fire yet.

I would be hovering by the first time I tried, just in case. A couple weeks ago, I was baking pies. My applie pies always bubble up and leak on the bottom of my oven, so I've started putting foil on the rack underneath. This time, I didn't know where I had put the foil, so I thought I would stick parchment paper under there. That's for the oven, right? And it was such a nice wide roll, the piece fit perfectly. So after, maybe 10 minutes, I started to smell a burnt smell. No way, I'm thinking, I CAN'T be burning these pies. So I kind of ignored it. Well it got smokier, so I thought I'd better see if it spilled over the pie plate and the parchment paper. That paper was dark brown/black!!! I almost set my whole oven on fire! I must have gotten it out just in time. And worst of all, the neighbours were over to watch the hockey game. How embarassing was that?

Covering in foil works great.
I've also made my own rectangle or weird shaped pans out of pop cases or boxes...cover totally in foil and it works great.