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To determine what is causing the overheating, you should first separate the coil from receiver and extend it on wires. Only place the coil on TX and then check temperature. If the temp drops considerably, issue is likely due to AC field entering PCB, battery, or other parts of housing.
To reduce AC field heating, the shield of the coil should be positioned to protect as much of the circuitry as possible (in particular, metal objects that may interfere with the magnetic field). Larger coils will do a better job at shielding the rest of PCB. Additional shielding can also be added behind the RX coil or over other parts of the housing that have a lot of metal. For shield material, consider Wurth Electronics 354002 or similar.
If extending on leads does not reduce temperature, then it is due to loss in the AC to DC conversion. There could be multiple issues here. The coil could be overheating due to incorrect values of the C1/C2 capacitors or DCR loss in the coil itself. See the link here on how to select C1/C2 capacitors. Using low ESR capacitors and multiple capacitors in parallel will help to further reduce the loss (recommend 3 caps in parallel for C1). At high loads, the receiver IC and other ICs like linear battery charger will also generate heat. Adding a better PCB heat sink can also help here. At higher currents you should use larger coils with low DCR to reduce heating. In the design try to keep the coil to coil distance low for higher efficiency and better thermal performance.
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