You may want to check out brewpi - it's a fermentation monitor, but isn't limited to just fermentation. The temperature devices used are DS18B20 temperature probes. You can get these pre-made in waterproof housing from sellers on ebay - the project also has a shop that sells them. The manufacturers claim they are accurate to +/- 0.5 C, although my tests against a calibrated thermometer show in practice they are accurate to +/- 0.1C.
Although the BrewPi project mainly touts the raspberry pi as the main wireless device, you can collect the results over any serial interface, such as a spare PC, or a linux-capable router.
The project logs data into pretty graphs so you can see the temperature now, or review later for any unexpected swings. I know the code well - it would be possible to alter the code to send a message when the temperature rises above a pre-set value. You'd then code a java app on your android phone to handle this message.
EDIT: I didn't mention, these probes are digital - they communicate temperature using a digital protocol called OneWire. The advantage is that you can connect multiple sensors to the same 3 power/data lines, and they produce much less noise over long cables compared to analog sensors like the LM37. The disadvantage is that you need to implement the OneWire protocol - e.g. use a OneWire library. This is the approach taken with the Arduino in brewpi, which has a ready available OneWire library.
If you are using a fan, the brewpi can control the fan to increase the rate of cooling when necessary. The controller uses a predictive algorithm, which avoids overshooting, and is much more accurate compared to a simple on/off thermostat algorithm.