There we have it! Final tally:

Vapor Chamber

Large piece of flexible graphite to spread out hot spots on the back of the device.

Large piece of flexible graphite to keep the OLED display in an isothermal state.

Several smaller pieces of copper foil to distribute heat, and provide some more grounding points for the device.

If you have any questions please leave me a comment! Thanks for checking this out!

Quick Edit. Added an image of the battery per request in the comments. Cheers!