I live in two stories. It is -7 outside. I have hot/cold water on my first floor but only cold water on my second floor. The pipes in the basement all seem warm. The heat is working. I have a feeling an exterior wall pipe might be frozen. What do you recommend?

You have a frozen hot water pipe to the second floor. That pipe is in an exterior wall.
What do you have on the second floor?

If it were frozen you would get NO FLOW (or very little) from the hot water line at all to the upstairs, in which case you would leave a hot water knob handle open while you unfreeze and insulate the frozen line. If you have flow then properly insulating the line will solve your problem.

The easiest thing to do is let a hot water line run until it gets hot, if you have flow. We let ours trickle all the time when the temps get below freezing which where I am is not very often.

Verify if your line is frozen or not, and plan to have that exterior line properly insulated. Here are some interesting videos.

how to unfreeze an exterior hot water line - Bing video

Doesn't sound like you have a frozen pipe but let us know. Not unusual to have hot water everywhere but the farthest reaches of your home, and it may take longer to get the already cold/cooler water flushed from the line.

Good Luck.

What exactly happens when you open just the hot faucet on the second floor, is there any flow at all?

Pam,
I suggest you locate your water main shut -off valve, or second floor isolation valve, and make sure they work and you know how to use them. Often, a pipe will freeze and not burst, but sometimes, a pipe will freeze and split and not leak until the ice melts.
I also recommend turning your heat up as high as possible to help warm the cold area near the frozen pipe.