Where is the heat from the hot component actually going to go? What's your cooling strategy?
If you can, perhaps it would be more effective to cool the hot component by conduction, maybe via a thermal pad into the enclosure, rather than relying on trying to localise the heat. It has to get out of the PCB somehow, and it can only help if you can provide a path that doesn't involve going through the 'cold' part of the board.
The board is the next version of a UAV control system that I use in my research, so it usually sits within a small plastic (3D printed) case so the convection is not very good.
I wonder what digital part nowadays draws 500mA (of 5v or 3.3V I assume) and dissipate that amount of heat into the board. 35mm x 35mm will run pretty hot with that. You surely need to use thermal filler pads to get the heat to the enclosure or some form of heatsink.
That would be the combination of an Cortex-M7 (STM32F746 @ 3.3V) at full speed, SD card, CAN transceiver, flash storage and a few LEDs.

It's not that bad though, its around 200 mA during normal running conditions and about 400 mA worst case (CAN short, + write on both flash memories).
You can also just omit the ground plane under the analog part. Most likely. Its not like you are really going to need it.
Copper conducts some 500+ times better heat than FR4. But it is not that thick.
That is actually a good idea!
The analog part is its own small region with the LDO driving it, so it does not really need the plane.
Just for reference, I added the images of the design to give some context.