A cold sandwich filling turned hot and bound is the whole concept of the tuna melt hot sando. It takes the sealed-pocket format from the baseline hot sando and fills it with the Japanese tuna-mayo mixture, tsuna mayo, plus cheese, then presses the parcel until the outside toasts and the inside fuses. Tsuna mayo on its own is a cold filling, soft and creamy; running it through the press with cheese converts it into something molten and cohesive that behaves nothing like the chilled version on a convenience-store sandwich.
The defining craft issue is moisture, because canned tuna and mayonnaise together carry a lot of it. The tuna wants to be well drained and the mayo dressing kept on the firmer side, because a wet mix will steam the crumb into paste and slacken the seal. Cheese is the fix as much as the flavor: laid over the tuna, it melts under the press and emulsifies with the warm mayonnaise into a thick, stable filling that holds a clean cut instead of oozing apart. The crimp has to be firm, since a loose creamy filling under internal heat will hunt for any gap. A good tuna melt hot sando cuts to show a hot, unified, faintly golden interior with the cheese threaded through the tuna, framed by a crisp toasted shell that contrasts the soft savory center. The poor version is unmistakable: an oily, lukewarm core where excess liquid stopped the heat from setting the filling, or a split seam leaking warm tuna mayo onto the plate. The inside has to be hot all the way through, not creamy at the edges and cold in the middle.
Common adjustments stay within the savory-creamy register: a little corn for sweetness and bite, black pepper, finely diced onion, a sharper cheese for more pull, a stripe of extra mayonnaise on the bread exterior so it crisps deeper in the press. There is also a melt built on a thicker tuna-and-mayo salad loaded with egg, which turns it dense enough to read as a different filling entirely, and that build is enough of a distinct experience that it deserves its own article rather than being crowded in here.