An apparatus is provided for splicing together old and new thermoformable sheets in order to supply a continuous thermoforming operation. The apparatus is used to join together thermoformable sheets by: providing a first thermoformable sheet with a trailing edge and a second thermoformable sheet with a leading edge; forming a terminal edge portion with a hot element along the trailing edge and a complementary terminal edge portion along the leading edge by severing a scrap sheet from each portion; laterally retracting each scrap portion away from the trailing edge and the leading edge; and joining together the first thermoformable sheet and the second thermoformable sheet by interlocking together the terminal edge portion with the complementary terminal edge portion.