Even a fridge is not needed. Put the milk+yogurt mix container in a clay pot placed in a tray of water, and it will turn into yogurt.
Anything fancier on top is just to reduce the amount of work needed or have longer fridge life.
On a different note, I grew up in Eastern Europe before it became capitalist and used to spend my summer holidays in the countryside. Needless to say,almost nothing was pre-packaged or ready made and everything was made from scratch, including yogurt. I can't really remember exactly how my grandmother made it, but I think she followed a similar process. I remember very fondly how it tasted, cool and slightly tart on a hot summer day; obviously these memories make me want to try it even more!
Somebody once told me that smokers smoke hoping that each cigarette will taste like the first. I can't really comment on that, but personally, every time I eat yogurt I hope it will taste like it did in childhood.
You just need good bacteria to start with, called the "culture", for your next preparations you can just get a sample from your previous yogurt.
The yogurt you get from stores with preservatives and ultra long shelf time, a.k.a. all bacteria is cleaned up to prevent it going sour, wont work, find someone that has real yogurt.
The problem with using yogurt from the last batch is that usually there is nothing left when you finally get to making the next batch... :)
Boiling the milk also helps the bacteria to work faster.
UHT milk tends to be sterile, if it's straight from an unopened carton.
Also, it's fun.
1. Boil milk in a pot (3-4 liters). Forget it's there. Turn it off when someone notices it boiled.
2. Wait till it cools to ~40c. Try to put a finger in the milk. If it's cold enough so you don't have to take your finger out, it's about ready.
3. Dump a cup of probiotic yougurt inside and stir.
4. Cover with the lid. In the winter wrap it with some blanket to keep it warm (probably not really necessary)
5. Wait for 24 hours.
6. It's ready. Put the whole thing in the fridge.
Somehow this works every time... It's seems really hard to ruin the process, and not for lack of trying...