The Adriatic off Montenegro is coldest in winter (around 10–14°C) and peaks in August at roughly 25–26°C — warm enough to feel more like a pool than the open sea.
In June the water is typically 20–22°C, which most swimmers find comfortable, especially after a few sunny days. By early July it climbs to 23–24°C and stays in that range through late August. September cools slowly: expect 23–24°C in early September, dropping to around 20–21°C by the end of the month. October falls below 20°C and organised beach facilities largely close.
For the warmest swimming, plan your visit for the last two weeks of July through the first two weeks of August — that's when the sea at spots like Becici, Jaz, and Velika Plaza feels at its best.