Mogsie, it would make sense that in summer your pond would be warmer at the surface, assuming very still conditions, no pump. Although I'm not sure how accurate the human body, and human interpretation would be as an accurate thermometer. I'd be interest in results if you measure your bath, but I'd be betting serious cash that you couldn't get a bath to stratify in any conditions other than laboratory.
Minnowman has the answer with density. Water is most dense at 39F. So, if calm, that water falls and colder water rises. The coldest water, 32.1F rises right to the surface and freezes. Most of us know about warm water rising but that's only true above 39F (4C). It's because what we were taught isn't exactly right. It isn't temperature causing all this, it's density. Temperature is only one thing that affect density. It isn't actually true that warmer water rises.
Ground Effect
However, heat from the ground, while it does transfer heat to the pond, doesn't affect stratification. At the bottom the water would be 39F, the ground then heats it to 39.1F and what does it do...it rises, because it is less dense, into the cooler water above and it cools. It isn't the warmth in the ground making this work. Strangely enough, if the ground under the pond were frozen, which can't really happen, the exact same process would occur. The 39F water touching the bottom would cool to say 38.9F and it would also rise, just as the 39.1F water did. Of course in this theoretical case the pond would freeze solid in short order. Just shows how strange water acts.
Also, sun light coming through the ice, assuming little snow, would warm the water right under the ice causing that water to sink.
It's purely density that causes stratification, and of course still water is needed. I'd say the ice cap is essential for thermal stratification in 3', 4' deep ponds. Even the fish being motionless on the bottom is important.
Opening in Ice
I assume keeping an opening in the ice would break any thermal stratification because there would be movement. Certainly a pump, I'm not sure about a heater on the surface, depends on exact setup. It could make the entire water column colder than 39F, maybe very close to 32F depending on conditions. With salt at 1ppt the freezing temp drops to 31.899F so in that case the water could be below 32F. At those levels we're getting into where fish can't survive. They can take temps below 32F, but not for long periods.
This is kind of why I'm a bit concerned with the thinking that a hole in ice must be maintained. It takes a while for the lack of gas exchange to become a problem. It's a tough choice, but I think it should at least be an informed choice.
Salt
I've forgotten about the exact effect of salt so I
looked it up. Water with 1ppt salt (0.1%, normal pond deal) would be most dense at a little higher temp, like 39.5F. So I assume 1ppt salt would make the bottom a bit warmer. BUT, I don't think I understand the whole story so I'd take that with a grain of salt. I live in Phoenix, so I'll leave it to others to research the real answer.
