My wife has a little cement pond with plastic liner that butts up against our house. It faces the south which is exposed to sun most of the day. The water does get hot, although our air conditioner system condensate water drips into the pond to help with make up water so that may help keep the temps down a little. It has filtration and a small flowing water fall, along with an air pump for aeration. Only about a foot deep at the deepest and less in part. Maybe 4'x8'.
I have thrown in various fishes in there at times, FHM being among them. At other times 2" BG and RES. She usually keeps some goldfish and a Plecostomus.
Have not really had a problem with the fish dying. Surprising actually how they mostly lived. Edit: she only keeps this pond going in the summer. It is drained for the winter.
Now reproduction I'm not sure about. The FHM might only reproduce when the water temps stay in a suitable range. FHM place eggs on the under side of things, so some substrate they can use as a nest and as shade would be important.
If you go to youtube and search for "Fathead minnows breeding like crazy" there used to be a video that showed them laying eggs in an aquarium, and usually other videos of raising fatheads will pop up in the right margin. Or a search for "raising fathead minnows" will get lots of videos.
Here it is 
