Hi Tomek, I find one needs to give lots of heat when warming milk, especially when using a bath method. Keep in mind the bath water will cool a lot when overcoming the cold milk. The milk warming will stall unless more heat is given to get past that plateau.
Most cheeses need to be cultured for flavour and acidity. The milk needs to be acidic for the rennet to work. Some cheeses use citric acid instead of a culture to get to the right acidity for the rennet. Once the milk is the right temperature and proper pH, the RIGHT amount of rennet ...not more...should be added. Too much rennet will make your cheese bitter.
Your milk type and quality will also affect good curd formation. I had to find a new source for good milk a few times before I was making consistently good curds.
Lastly, I hope you are following a good recipe to make your cool cheese... Not all recipes are written well and will misguide you from making good cheese. For cheesemaking, it's the little things that make a big difference, following proper basic cheesemaking guidelines and recipes accurately will bring success. If you want, post your step-by-step recipe here so others can help here with good input.
I hope that helps... Have no fear, we will get you on the path to good curds
F