That will be nice to know.
You may need to mechanically affix the heat sync to the 7805. Something like a small screw, alligator clamp, etc. should do the trick and help dissipate the heat.
If/when you get your scope, hopefully it's a 2+ channel. Then you could run up both and look at the signals. You should be able to see any variance or drift.
But, then again, maybe it doesn't matter... It's only used for bench testing.
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