That is likely way too much for a J310…
I think your problem is that you have it mounted upside down. The gravitational effect on a Chinese transisters beta is known to be asymetrical. 
Depends on the application; in this case, the variations in the DC bias current of the transistor are not multiplied by the gain of the device, so they are below the “magic” 10dB line where that current noise would contribute. It is also bypassed by the 220pF cap at HF and VHF frequencies.
I agree that metal film would be much better for precision DC or near-DC circuits. Analog Devices AN-940 has some useful insight on this, too.
ON Semi claims 350 mW at ambient 25 degC.
LOL
Ah, but was that claim written by their engineers or marketing folks?
If the U310 metal can was hot to the touch, the to92 plastic of the J310 would be a bad radiator of that much heat, IMO.
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Don’t forget that even though the package might burn you, the silicon is happily working. It may not be the ideal situation for you, but often it isn’t a problem.
The rated junction temperature goes up to 125 C which will register as a lot worse than hot!
Bingo! It was the trimmer cap (the white one) … I swapped it out for a Murata red-colored one (4.2-20pF) and was able to find the +12dB peak gain point.
If I were to re-build this, I’d invest in a piston trimmer to make it a bit easier to align.
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What was the cap value when you achieved the 12dB gain?
Was it the value of the cap or something to do with the construction of it that caused the issue?
Two problems conspired to make it hard for me to find the gain peak: the trimmer cap I was using had a range of 4.9pF to 75pF in one turn, and the Q of the output match circuit is fairly high (narrow b/w). Using a non-metal tuning stick, of course, I wasn’t able to get the peak.
I swapped out the cap with a 4.2pF - 20pF one turn model and, lo and behold, I could get the peak!
I’m planning to swing by Tanner Electronics today to get a 5-20pF piston cap, which should it far easier to align it.
The input tuning appears to be much broader and easy to align.
Here’s a good reference on Resonance, Q, and matching for those who need a refresher (or an intro).
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Dunno, as it is currently soldered in, but simulation predicts 9pF. That’s in the range of the 1-10pF trimmer specified in the schematic.
Ah, I thought you were using the 3-15 pF cap in the schematic and needed more range.
Nope, too much cowbell!
Done! $0.59 each. Will solder in later today and check on the big SA. Gain plots to follow.
Signal generator was set for -40dBm, with approx 1dB of cable loss.
Gain peaked with the Red Murata cap:
Gain peaked with the piston trimmer:
So, we’re sitting right at the 11dB gain figure. Unfortunately, the piston trimmer is more sensitive to the lid being near it, so the gain w/o the lid is right about 12dB. I haven’t found a good way to mount it to avoid this problem and still be able to get to the screw with an adjustment tool.