The temperature has been considered in the allowance for the overcurrent protection.
Jim, are you saying that 14/2 would handle a welder that needs at least 40 amps to run.
So now you have another issue to report in addition to the breaker side at the panel. The 50 Amp rated receptacle is wired with 14G conductors. What load different equipment plugged into there can draw will vary widely. If it’s hard wired into a welder is one thing, then the welder’s requirements come into play. If it’s wired to a receptacle though it needs to meet the requirements of the receptacle because he could plug anything with that configuration into it now, and nearly everything with a 10-50P configuration is going to be a problem for 14G conductors.
The code issue is with the OCPD size. The 50 amp single receptacle and #14 conductors could be code compliant with the proper size circuit breaker.
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Check this one out that a sparky installed.(He left his calling card). I removed the drywall above the panel with the owners approval and found the #6 going into a junction box with 4 10-3’s coming out. There were 4 240V outlets in the garage in single gang wall boxes (which is why it looked suspicious to me). The owner said he had them installed for a welder.
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The motto says everything one needs to know 
I mean he literally tells you that you will get shocked after paying him
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That panel had issues even before the #10 cables were added.
There are situations where circuit breaker ampere ratings & wire size combos that are permitted by the NEC but are not OK for normal branch circuits, such as motors, A/C equipment, & welders, they also allow 14 AWG to be used for 20A, 12 AWG 25A, & 10 AWG 35A, 14 AWG on 50A I doubt is OK, but there are times when the data plate on A/C equipment could allow 12 AWG on 40A, it all depends on the minimum circuit amperes & the maximum fuse or circuit breaker listed.
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