Electric arcing creates a huge temperature in the air around it. When lightning strikes planes, why doesn’t this high temperature air melt/deform the aircraft skin? Also can these high temperatures ignite fuel in the wings?
Potentially, yes, but this would be a very rare event. The principal reason that lightning does not create damage to an aircraft is that the airframe, particularly aluminum airframes, are electrically conductive, and carry the charge easily around them with very little resistance, which would otherwise create heat. Essentially, the airframe behaves like a Faraday cage and protects the contents within from damage. The airframe is also designed to dissipate static electric charges through static wicks, lightning runners and lightning spikes on the exterior of the skin. Fiberglass parts such as radomes are protected by lightning runners which carry the charge and protect electronic components underneath. Composite aircraft made from e-glass are constructed with a stainless steel mesh ply imbedded in the skin which channels and carries electric charges.
Lightning strike protection is a critical part of aircraft certification under parts 23, 25, 27 and 29. Very rarely has lightning caused any kind of an accident, and commercial aircraft are frequently struck by lightning every year and suffer almost no ill effects from it.
The other answers mention aircraft have a high electrical conductivity. However, air has a much lower electrical conductivity and does get hot, as you mentioned.
The hot air causes little damage because:
- The electrical current only heats a small area of the air for a brief period.
- The air expands quickly, causing it to cool quickly.
- The aircraft moves quickly, so it is only exposed to the heat briefly. After that, it is exposed to very cold air that can remove the heat.
- Since the aircraft skin is electrically conductive, it also conducts heat away from the hot area.
Why doesn't it punch holes in the fuselage? It can.
Can it ignite fuel in wings? Yes, lightning creates sparks that can potentially ignite fuel vapors. The liquid fuel itself does not ignite, but the vapors can.
Both of these things are extraordinarily rare, however. Planes are specially designed to be resistant to lighting strikes, and most lightning strikes result in little to no damage.
When electric current flows through a medium, the amount of power dissipated is inversely proportional to the resistance of the medium. This is why the heating element in a space heater heats up, but the power cord leading to it doesn't (much): the element has a much higher resistance than the cord. This is also why using too small of an extension cord for the load can cause a fire: thinner conductors have a higher internal resistance.
Air has a much, much higher resistance than the aluminum, composites, etc. that they use to build planes, and hence gets much hotter during a lightning strike. This is easily seen in videos of planes being hit by lightning, where the air glows from the heat and the plane doesn't. Furthermore, heat can't transfer from the air to the plane because it's almost immediately blown away by the slipstream.
Of course, that's not to say that it's impossible for lightning to cause damage, because it absolutely can. If the current finds a spot of higher-than-average resistance, or gets concentrated to a point, it can (and has) caused significant damage.