Another big +1 on the arduino. If you're looking for something (relatively) out-of-the-box, the board equill mentioned earlier looks quite good. But arduino is definitely the Mr. Beer of embedded micro controllers. I've moved on to slightly more complex things, but I still use the arduino to prototype new designs or when I'm in a hurry.
The arduino is basically just a microchip with a bunch of in/out pins (some digital, some analog) that can be controlled by a piece of software. It's got a usb port, which makes it easy to program. If you've got a grip on basic C, it's relatively simple to program it to read sensors, drive servos, process data, run LCDs, etc. It would handle the kind of project described in the OP quite handily. I've got something similar running in the other room right now.
The arduino will hook up to a computer to feed data directly via USB, or you can connect it to a network via Ethernet or wifi. Networking makes things a bit more complicated, but still manageable. A relatively simple setup might look like this:
Arduino ($30) - brains of the project; reads the temperature probe, processes logic to turn on and off the relay that controls the heater/cooler, sends data to and receives commands from your web server. There are cheaper options, but they require a bit more investment in equipment and a bit more knowhow. If you have access to a digital programmer, for example, you can build something with the functionality of an arduino for about $10.
Server interface ($0 to $60) - The cheapest and simplest solution here is to just have the arduino feed data to a computer over USB. This requires a computer next to where you'll be fermenting, but it's cheap and straightforward. At the other extreme, the very cool $60
WiShield from Async labs will let you run your arduino as a server over a wireless network. You could either host a web page directly or use it to feed data to another site. You could do the same thing over
ethernet for about $25 in parts. If you're more ambitious, you can save money by using an XBee radio network, but that gets complicated.
Temperature sensor (<$5) - There are a lot of options here, but I'm a big fan of the 1-Wire sensors (like the DS18B20). I've used thermistors and other analog components before, but if you want a long cable on your temp probe it can be a major pain to manage interference properly.
Relays (<$5 to $20; need two if you want both heating and cooling control) - If you want to control a heater or a cooling device from your arduino, you need something to switch the AC power coming from your wall on and off. A relay is basically just a high-power switch controlled by a low-power signal. These can be built relatively easily, but if you are unfamiliar with electricity I would encourage you to consider buying something prebuilt like
this. None of this other stuff is dangerous. If you screw it up, at worst you'll just fry your equipment. The 120VAC/220VAC coming out of your wall can kill you if you don't know what you're doing.
Miscellaneous wires, resistors, breadboard, etc. (<$10) - just stuff to connect everything up.
Let me know if you need help finding specific parts or want more info. The board equill posted is probably easier and possibly cheaper, but arduino gives you a lot of flexibility. I'm working on a system right now to control my stovetop HERMS, have another that ferments yogurt in a crockpot for me, and yet another to let my young son control the music in his room. None of it is that practical, but then again not much we do here is
-malfet