How do I install the factory joint which is thicker than the heater wire?
Install the factory joint splice in the floor.
If it is not installed in the floor, the joint may give and your system will no longer work. In addition, your warranty will be voided but you will have to repair the splice and place it back into the floor. This factory splice connects the heated wire to the unheated lead. NEVER leave it exposed to air and do not place it in or behind the wall.
To eliminate the difference in height between the heater wire and splice, cut a channel in the subfloor to place the joint in. Encapsulate the splice completely in thinset. Please consult the installation manual of your heating product for more information.