I don't have much experience with Arduino yet, and was hoping for some advice on the heating part. I have a standard PSU which supplies 12V (400W), and currently have three coils of NiCr wire that should provide sufficient resistance. In his example, the wires are put in fire cement to keep them in place at the bottom of the aluminum box.
Does anyone have advice how best to connect this? I guess I'd need a solid-state relay of sorts> Are there perhaps better solutions? I noticed these type of heater cartridges, but I guess only the tip gets heated? Also there are heating pads, but I guess they will not generate enough heat?
Those heater cartridges would be a good choice for a project like this -- much better than using bare, nichrome wire. Find a high temperature adhesive or some kind of metal strap and attach them to a plate of aluminum that the bottles will sit on. The aluminum will help disperse the heat evenly and much more quickly than MonkeySailor's design which uses fire cement. The fire cement is overkill for something like this anyway -- perlite with just enough plaster or concrete to hold it together would be lighter and still be a good insulator to prevent you from burning your table. You can also find high temperature (300 or 500oF) caulk at hardware stores for use with fireplaces.
The specific cartridge you linked is not the best product though; you should be able to get a pack of five or ten for close to the same price. You'll only need about 100W to keep things warm but it'd be nice to have more than one to help spread the heat around and avoid hotspots.
So you recommend to use a MOSFET for control, perhaps something like this?
As for the heater cartridges, I agree that glueing it with a high temperature adhesive is best for heat dispersion. I could use fire cement or your perlite/plaster mix to insulate toward the bottom.
You can get a whole bunch of them for cheap. I do feel that the tips are a bit small though, which might create hotspots indeed? Also, can I just hook them up on on 12V line and control them via the MOSFET?
You need a "logic level mosfet", IRF530A is not. It looks like it might work with a 5V gate but there are better choices out there. Look for something named IRLxxx or search the forum for suggestions on specific parts. "What mosfet to use" is a kind of question that has so many possible answers that no particular answer can be given
Those heater cartridges don't heat just the tip -- it's really the sides that emit the heat. If you look at pictures of 3D printer hotends you'll see that the end is usually sticking out the side or otherwise not in contact with the aluminum block. Here's a textbook example: Heater Block with Screw-On Thermistor by rp_one_labs - Thingiverse. And as an addendum to that the particular size and wattage of heater cartridge you linked is popular specifically due to its use in 3D printers.
) MOSFET and experiment a bit.