K-Type thermocouple to bluetooth?

I recently purchased a wood stove that has a temperature sensor on it for the operation of the catalyst. The sensor plugs into a little LCD display via a k-type thermocouple plug. Is there a way to send that data to a more reliable display source, like say a phone or RPi 7" monitor? The LCD provided with the stove powers off after about 15 minutes, since it's only running off a 9V battery. I wanted something like a picture frame on the mantle displaying the temperature all the time.

Thermocouple plug looks like this:

The catalytic temperature monitor looks like this:

Thermocouple -> K-thermocouple amplifier -> Arduino -> Bluetooth or any other output device.

Examples of all parts of the project are readily available through Google.

Of course, project power is subject to the same sorts of limitations as the display you already have.

Hi, I am using K thermocouples on my woodstove and kiln.

How-TO HERE: http://arduino-info.wikispaces.com/Brick-Temperature-Thermocouple