Not a problem. I encountered just this situation bike touring in the Black Hills. I sat down, boiled water,poured it into a bottle, placed the bottle back in the stream, where it cooled while I boiled another pot, etc. until in about twenty minutes I had something like two liters of cool water. Of course, about two miles down the trail I encountered an approved source.

If I am really dehydrated hot, water of any temperature works, although cool is better.

It is a good idea to have alternatives (think Aqua Pure), but boiling is simple and effective, allowing me to apply my brain power to other problems