The Nexans/Olex Cables 2019 cable catalogue.
This catalogue may also be downloaded from Nexans's own website.
NOTE: This catalogue is being used as an example of a cable catalogue, and not as a commercial endorsement of Nexans and Olex. The behaviour of other brands of cables should be similar.
This catalogue has a range of information from AS/NZS 3008 about cable selection, voltage drop, and short circuit current withstand.
At low currents (<100 A), the cable rating is generally defined by the protective device rating.
At higher currents, the protective device can be programmed to accommodate the cable capacity.
In general, for most low current jobs the "rule of thumb" section C3 in the Wiring Rules may be used.
I would advise that for any household wiring, that the "bulk thermal insulation, partially surrounded" rating is used. This covers wiring in contact with the surface of thermal insulation, as well as cables between thermal insulation, and a non thermally insulating surface (e.g. cables clipped to wood and in contact with thermal insulation).
For TPS, the most relevant pages are pages 44-45. The ratings for "surface clipped" (the right set of columns) mostly corresponds to "in air" ratings in section C3. Note that the rating may vary depending on the interpretation of AS/NZS 3008, and the exact construction details of the cable of interest.