With this complete, I modified the example to log multiple readings at a fixed rate and store the values into an array in memory.
As an aside, the Bluetooth module which I used has a great interface. There are 4 pins. 2 pins plug into PWR/GND. The other two pins act as Serial RX/TX pins. Normally you would plug the Bluetooth module into pins 0/1 which are part of the Arduino's hardware serial support. Instead, I decided to use pins 2/3 on the Arduino. This is possible thanks to the SoftwareSerial library.
With the Bluetooth module connected, I added code to regularly check for an incoming message and respond with a dump of the saved readings. This is what the completed circuit looks like.
The complete code for my Bluetooth temp sensor is available here.
