I'm trying to figure out what's the max temperature that an already caramelized sucrose solution can be heated to, so it remains liquid after cooling and its thicknes is maximized.
There is no such temperature; caramel is not liquid*. Sucrose solutions stop being liquid at temperatures well below the caramelization temperature.
If you need liquid caramel, there are ways to achieve it, mostly by using sufficient acid, or by making a caramel sauce by diluting the already-prepared caramel with dairy. I suppose you could also achieve it by adding water post-caramelization, but you would have to be very exact in your ratios. But you cannot get it by temperature control only.
* if you wish to be very pedantic, even the darkest caramel is liquid, but only in the sense that church windows are supposed to be liquid - you have to wait for years for its drip to move a few centimeters. This factoid has no practical use for cooking, but it may help you clarify your concepts - your phrases "remains liquid" and "thickness is maximized" actually point to a state of matter which is probably not the one you wanted to achieve.