L-Adapter

You need data. Measure the load's current demand with the DMM in series Ampere mode first. To see if its more than it should explaining the dissipated heat. Don't forget to place the red jack in the DMM's special socket for current measurement. Another reason would be having unnecessarily high AC secondary transformer leading to high DCin-DCout across the L-A even when the load's current demand is what you expected. You can verify the DC difference across the reverse protection diode D11. Do that when actually powering the application. If the mA consumption proves normal, augment the sinking because its much cheaper than changing the transformer.

*Any loss on the output cables is dissipated on the cables not on the sink. You can also measure the voltage drop across the beginning and end of the output cables while working. If its significant, use thicker / shorter ones.
Thank you ever so much for the detailed reply, I appreciate it.
It is showing 9.7V in actually.
According to my cheap DMM, the max draw is 1.25A even when booting the USBridge Sig.
It powers nothing else now. Only a USB stick.
D11 reads 6.84V while playing music.
 
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It draws enough current while booting. But 1.25A startup in a 500mA spec digital device is still logical. You have voltage space (judging from the D11 reading) to use a lower VAC transformer reducing dissipated heat or keep it and augment the sinking someway. Taller sink, external sink, something.

*Is 9.7V in you mentioned the transformer's AC voltage going to the L-A?
 
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It draws enough current while booting. But 1.25A startup in a 500mA spec digital device is still logical. You have voltage space (judging from the D11 reading) to use a lower VAC transformer reducing dissipated heat or keep it and augment the sinking someway. Taller sink, external sink, something.

*Is 9.7V in you mentioned the transformer's AC voltage going to the L-A?
Yes. 9.7V is the trafo AC into L-Ad.
I thought it was closer to 9V.

Thank you again for your advice.
 
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It should be near 12V DC rectified and the difference to 5V burns on the sink at enough current rate by your device so it gets hot as expected. You haven't done something wrong in the build. 6.84V difference at 500mA is 3.42W. It takes more sinking or a 7V AC transformer to decrease the heating.
 
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I seem to be running a bit hot in comparison to others.
I bought the full kit from Tea Bag and sinking on board with those.
The sink is too hot to touch and according to my DMM, 70C (16C Ambient)
10V in 5VDC out.
Powering a USBridge Sig with it. Which then powers a Khadas Tone Board (which asks for a 500mA power supply )
I tried removing the KTB, but it only made a few degrees difference.
Would quite long DC cables cause it ? (I forgot you advised short as possible.)
Thank you for your advice.
I got hold of an EI trafo for now.
It gives 7.2V loaded.
The central span is still quite toasty, but i am a lot happier.