From at least the 14th century on, when we first have examples of surviving padding, helmet padding worked as both padding and a suspension system.
Thickness varied, with field helmets sacrificing padding thickness for comfort during long wear, and helmets for jousting and other specialized combats where the helmet would only be worn for a short time making the opposite choice. Even so, padding for the skull as thick as a modern potholder was probably at the upper end of the scale.
Typically, the crown of the helmet padding was divided into 4-10 segments laced together at the top to provide an adjustable fit. The lacing could pass through eyelets at the top of each segment, or between the inner and outer layer at the sides of the top of each segment
The robustness of the cloth used seems to have ranged from no heavier than a work shirt to significantly lighter than painter's canvas.
Rows of quilting could be either horizontal or vertical, converging like lines of longitude at the top of the helmet. The effigy of Philip the Bold of Burgundy at Dijon is one example of the latter system, and Churburg bascinet #15 is a surviving example. Alternatively, there could be a vertical line of stitching at the middle of each crown segment with parallel lines of stitching on either side. Lines of horizontal stitching seem to have frequently been about a finger's breadth apart. Some were stitched both horizontally and vertically.
The quilting stitches could present a continuous row of stitches visible on the inside of the lining, stitches visible on the inside separated by a gap of similar length, or very short widely separated stitches visible on the inside of the lining.
Here is a good detailed view of the lining of a sallet at Leeds.