The one issue I found was that whenever I was connected to the base station over Bluetooth, the base station was unable to receive temperature readings over the 315MHz RF link.
This is what the setup looked like when it didn't work.
In the end I posted to the Arduino forums and spoke to some friends about the issue and concluded that the Bluetooth RF must be interfering with the actual circuitry of the 315MHz RF receiver. My first idea was to try and setup some kind of electromagnetic shielding around the 315MHz RF receiver module. However, before I began working on this I decided to try simply moving the Bluetooth module further away from the 315MHz RX module.