Total power: 12V * 0.25A = 3W
5V Regulator: (12V-5V)*0.25A = 1.75W
Thus the first regulator on the Panda, the 5V regulator, must dissipate 1.75W.
Heatsinks are rated at “temperature increase per watt”. It means that a 50C/W heatsink will be 50C above ambient if it must dissapate 1W.
The regulator doesn’t have a heatsink fitted as such, only some PCB area to act as a heatsink. The temperature rise will depend on the size of this area…
The regulator package without heatsink is spec-ed at 136C/W, so at 1.75W it will reach 238C above ambient. Not good at all.
One square inch of filled copper(no traces, solid) on PCB is 66C/W, so at 1.75W that is 115C above ambient.
It also means that your Panda is using 1.25W, and the regulator is turning 1.75 into wasted heat. Which means that your power supply has a 41% efficiency. Switching to a switching regulator will double your run time from the same battery…