Saturation of the water is determined by the partial pressure of the gas. In a sealed tube, heated or not, if the hydraulic pressure is high enough, bubbles won't form (won't displace liquid water) against that
We have no way of knowing if the
temperature rise expands the water more than the container (so gage pressure
rises with temperature) or if the temperature rise expands the
container more than the water (pressure drops with temperature).
Thus, as in boiling, there may be a superheated situation, where the water and its dissolved gasses are ready to erupt, but the container
(like a pressure cooker) holds it all in.
When bubble-formation IS favored, there can be a variety of reasons
that bubbles would form at a site. A surface that is 'wettable'
by water, would inhibit bubble formation, while one that is
hydrophobic would promote bubble formation (because there is less force holding the water to that surface). Any microbubble,
perhaps protected by a crevice, can nucleate a stream of gas
bubbles, as one sees in a pan of boiling water on a stove.
Or, the superheated liquid can form bubbles around the trail of
ionizing particles, as in a bubble chamber invention of Donald Glaser.
Once a bubble forms and grows, the immediate vicinity of that bubble is no longer gas-saturated, so the liquid and bubble are not homogeneous with the rest of the container. The next bubble may form in a richer
dissolved-gas portion of the liquid, elsewhere.