Bacteria can be cultured providing they have the necessary conditions ie a food source and a suitable temperature.
For the ideal temperature, you will need to check for the bacteria that you wish to culture. Take a look on MicrobeWiki. It is often around human body temperature for many bacteria but some require lower temperatures such as soil based organisms.
I have cultured yeasts such as Saccharomyces boulardii, probiotic capsules and oral probiotics for teeth health using milk and they produced very good yoghurt all at around 38 to 42C. The yeast surprised me how well it worked in milk. I have cultured bacillus subtilis using liquidized potato kept under 30C.
It is much cheaper culturing organisms rather than paying for expensive capsules.
The fridge is too cold to culture. A fridge is meant to lower bacteria growth and therefore to preserve food. Using a yoghurt maker is a better temperature regulator but not ideal due to the temperature often being too high for some organisms. I am planning on fitting a termperature regulator to my yoghurt maker to better regulate the temperature. They have sensors and digital displays which can switch on/off the heating element depending upon the temperature of the sensor. That should allow the temperature to be maintained at the temperature that I set so it should work better for organisms that require lower temperatures.
My yoghurt maker once nearly cooked the yoghurt I was attempting to make. It was taking far longer than usual and when I checked the temperature of the yoghurt it was over 50C! It must of been killing the bacteria which was why it was taking so long. Low 40's is as high as they should get. Human body temperature is around 37C. It just goes to show how crap the temperature regulation on cheap yoghurt makers is. A temperature control device should sort all that out and they cost very little.