Trout burrowing through the stream bed, wow. Wouldn't the water get warm from the exposed rocks acting as heat conductors? How far down are we talking about when they burrow?
No. I mean, normal freestone springs are the result of shallow underground flows, and they come out at around 55 degrees year round (ok, they do vary a few degrees, but not much). You don't have to get very deep to hit stabilized temperatures.
This is why streams stay cool in summertime! Small freestoners are largely spring fed and have portions of their flow underground throughout most of their length, and in steeper areas, pick up new springs more frequently. That's how it can be 75-90 degrees day after day in July and that little freestone stream is at 60-65 degrees. But as they get lower and larger and flatten out, it's usually on or nearly on bedrock, so there's more water above ground and less % below ground. The springs also come less frequently (they blew their load on the hillsides). So the streams warm. In any given area with freestoners, there's a semi-consistent "max size" for trout, where when a stream gets too big it also gets too warm.
The same thought process applies to limestoners, but there's no max size. Because the underground water doesn't have to be over the bedrock, it can be through the bedrock. Thus instead of hundreds of small springs spread out over a large area you can have 1 large one, where a sizable stream emerges all at once. Further, in the lowlands, flowing on bedrock does not mean water can't go down. The bedrock is permeable. So even largish streams can have large portions of their flow disappear underground and flow there long enough to cool down, re-emerging far away and rejuvenated.
So the difference is over bedrock for freestoners vs. under bedrock for limestoners. But even over bedrock is indeed deep enough to hit stabilized temps. Only need a foot or two for that.
Think of it this way. If temperatures don't become an issue in water that is above ground, it certainly isn't going to be an issue for water that is below ground. There are other, obvious issues they'd face. But temperature isn't one of them.