I know that SpaceX's Falcon uses TEA-TEB instead of a physical igniter, but if I remember correctly, NASA has never used hypergolic propellants to start their restart-able engines. How does NASA's (or ULA's, or Arianne's) rockets/payloads (such as the LEM) that require re-ignition achieve it without the igniter melting?
On the J-2, the spark igniter is positioned above the fuel injector face, in a small chamber above the main combustion chamber. It's apparently uncooled and actually operates continuously during engine firing. Presumably only a small amount of propellant is burned there, and a relatively large amount of cold propellant is flowing through that general area of the engine, thus carrying heat away.
The Apollo CM, LM, Titan Transtage, and other early American restartable stages all used hypergolic propellants, and so needed no ignition source; likewise I believe the Russian upper stages like Fregat and Briz all use hypergolics.