Different materials react to thermal cycles differently. Some aluminum alloys are time at temperature sensitive, i.e., extended exposure to high temperatures over ages the alloys thus they loses in strength, ductility, etc. Other materials are less likely to suffer adverse affects from repeated thermal cycles such as low carbon steel. Quenched and tempered steels may see many thermal cycles, but utilize maximum heat input to limit the size of the heat affected zone to minimize degradation of the mechanical properties within that region.
The welding engineer, with a substantial back ground in welding metallurgy, is usually well versed on how different metals will respond to thermal cycling (thermal history), heat treatments, etc. This subject is beyond the scope of training of most inspectors. There are times when additional resources are needed. This is such a case. The bulk of metals used on a worldwide basis is primarily ferrous metals such as carbon steels, low alloy steels, and high alloy steels such as stainless steels. They account for about 95% of the total tonnage used annually. That means nonferrous metals such as aluminum, titanium, etc. is used to a very limited extens, thus few inspectors have a firm understanding of nonferrous metallurgy. They may be ill prepared to respond to how nonferrous metals and alloys will respond to various heat treatments, heat inputs, etc. For that we rely on codes and specifications that are developed by "experts" in those areas. Granted, some owners do not do their "homework" and the specifications they produce for specific projects may leave us wanting, but welding standards developed by organizations such as AWS, AA, CDA, NDI, etc. are excellent sources of information on the subject of proper welding of a wide range of materials.
I have worked with titanium, zirconium, and aluminum. Some specification limit the number of thermal cycles and some do not. For additional information I defer to the organizations I have mentioned and I rely on the AWS Welding Handbooks as well as ASM references for information on those alloys for which I have limited experience.
I'm late for an appointment with a client, so I better run along.
Best regards - Al