Where can I find a temperature sensor that tweets?
There are many ways to do what you want.. but none of them seem very easy as networking remains quite a complex thing to use, wired or wireless.

Obviously you want to just plug in the power and forget about it.

Using the Raspberry PI is most probably a very good idea, Its cheaper version (Model A) about £20, it can run Linux, you can use a WiFi dongle with it. You can remote into it using SSH.. so yes it is actually a very good solution.

Not so long ago

Before the Raspberry the popular choice would most likely be Arduino Ethernet board on it. The costs are slightly higher for this though, There is a Library for use with network available making http communication pretty simple. The drawbacks as of today are obvious, much slower processor, no OS like Linux on it, no SSH, no wireless..(available with other shield + wifi module) and the costs start to pile up.



But today

I am still waiting for my Raspberry to finally arrive and then I can experiment with it. But from my understanding it does have GPIO as on the datasheet page 89 and are available on the PCB it self as double row pin headers. I suspect you can use these to read analog values such as voltages so you could easily connect a temperate sensor like LM335Z. I still have not seen any code on how to do that though but this does seem like the best solution now a days.



But having a few points for monitor can start to cost too much

The nice thing about Arduino still today is that you can buy a small chip like from the tinyAVR that is compatible with Arudino libraries to certain degrees. Using these baby MCU which have built in clocks(fairly accurate now a days)(cost about 1-4usd per chip)with a temp sensor and a cheap as chips 433/800mhz transmitter that sends out temp readings every hour or so. These guys can run on a battery back for 8-16 months. 
Then using the Raspberry plug in a USB 433/800mhz receiver and just listens to data and the OS level program decides what to do with. Store it in a database somewhere on-line and sends you tweets or text messages via on line gateways in case of emergencies.

This kind of project will require some design time but you could monitor up to 20 places in your home with a total project cost under 100USD ... hmmm. Pretty neat.

Ref:

Online Thermometer

Shrinkify Arduino