Size really matters: Soldering tips
As a starting point, RS Pro would recommend a tip temperature of 320°C for the Sn60 Pb40 alloy wire and 360°C for the Sn99.5 Cu0.5 alloy wire. People do use higher temperature settings to get faster melting/wetting speeds but the downside of higher temperatures is that the soldering iron tips will wear out more quickly. RS Pro advice is to use as low a tip temperature as possible (and to also use local fume extraction), but some experimentation may be needed to get the optimum setting for the particular application.
These are normally optimised to give the best results for each soldering application. The actual settings are determined by the solder alloy, the size of the components, the soldering iron tip size, the location of the components, the construction of the PCB and to some degree the experience of the operator, so every customer does things slightly differently.
The general rules are to use the largest soldering iron tip as possible for the particular application as the heat transfer to the joint and the solder is better and you should be able to use lower temperature setting. It is recommended to use the lowest temperature setting possible as high temperatures can burn off the flux too quickly and poor soldering could be seen due to increased oxidation of the joint. High temperatures also reduce the tip life and increase the risk of causing heat-damage to the component and the PCB. Keeping the solder iron tip tinned is important to avoid oxidation (which reduces the efficiency of heat transfer) and to prolong the life of the tip.
With lower powered irons, the heat at the tip can reduce more quickly when in contact with the PCB and component and will take longer to heat up again than with a higher powered iron. A lower power iron should be fine if the components are small, but for larger components or PCBs with ground planes for example which will take away the heat from where it is needed, then a higher powered iron may be better. As already mentioned, using the largest tip size you can is recommended.
With regard to industrial standards, the only mention of soldering irons I have found is in J-STD-001: Requirements for Soldered Electrical and Electronic Assemblies. Appendix B of this document is called ‘Guidelines for Soldering Tools and Equipment’ which gives selection criteria for benchtop and hand soldering systems.