press - type apparatus for thermally bonding thermoplastic sheet material workpieces is provided with a pair of opposed platen assemblies which each include an inflatable set of compliant diaphragm members , a pair of opposed heat sources which may be brought into and retracted from contact with the diaphragm members , and a source of pressurized fluid for inflating the diaphragm sets and for cooling the heated workpieces . the method for operating the press - type apparatus basically involves both heating and cooling the assembled workpieces while they are simultaneously being retained in a condition of being clamped by the inflatable sets of the diaphragm members .