Theoretically, 0 deg. Celsius. In practice, it depends on a few things like your altitude and the atmospheric pressure at the time (has a smaller effect on freezing than boiling, but still noticeable if you look very closely) and exactly how "pure" your water really is. Remember that when it comes to freezing, water is weird because of the way it forms its crystal structures as hexagons, with huge holes between the molecules. So any interference by salts or other contamination will inhibit the crystal formation and effectively lower the freezing temperature. Therefore, "pure" distilled water should have a boiling point of zero Celsius since the Celsius scale is defined by the phase change properties of water.

In addition to inhibiting the crystals by sheer geometry, contaminants like salts will also disturb the water's hydrogen-bonding structure where the hydrogen on one molecule will "stick" to the oxygen on an adjacent molecule and even though it's not a real chemical bond it will take some force to un-stick them. These bonds are strongest in ice, pretty strong in liquid water, and almost nonexistent in water vapor. So anything that disturbs the hydrogen bonds by altering the electrolytic structure of the solution will, generally speaking, make ice easier to melt and water easier to boil because there are fewer hydrogen bonds that you have to fight to remove. Since these salts are ideally not present in distilled water, DI water will have a HIGHER freezing point than water that includes dissolved salts.

If you've ever been in a snowstorm and the road freezes over, you can spread salt on it to dissolve the ice because the cleaner ice is harder to melt (requires more thermal energy to break those hydrogen bonds between molecules) than the salted ice. So, DI water freezes at 0 Celsius, while salted ice might melt at 20 Celsius and regular tap water might freeze at -1 or -2 Celsius. In theory anyway.

Actually I was thinking about how minerals are affecting waters ability of freezing and boiling. Have you ever tried to make an experiment with DI water? If yes, could you send your results? I would be very grateful

The issue is colligative properties of water, try a search on a chemistry book. No need for experiments.