A Hacked Gadgets reader took his Almost There project up to over 42,000 feet a few years ago and documented the process.  Looks like Near Space is gaining some popularity recently.

Here is a list of projects that are worth a look:

Near Space Project 1
Near Space Project 2
Near Space Project 3
Near Space Project 4

"So, here’s what I decided to do. Use a Pressure Sensor and a Temperature Sensor fed in to a PicAxe CPU that approximately once a minute will trigger the transmitter and bang out the raw data using simple Morse Code.

On the receiving end, I’ll use a matching FRS radio to receive the data, feed it in to the Sound Card of a Laptop, and a Cassette Recorder with sound level activation to record the data for time immemorial. Run software on the Laptop that decodes the Morse Code and displays it on the screen, and saves it to a Data file. Then (finally) I’ll have a conversion chart that I can look up the raw data values from the screen and manually convert them to Altitude and Temperature readings."