Unfortunately you need a work visa or permanent residence permit to buy a car in South Africa. For future reference, if you do end up staying in SA for longer and you then have a work visa or permanent residence permit, we have a pretty comprehensive guide here: Buying A Car in South Africa.
Thanks for getting back to us. Are you referring to the TRN process as outlined on the SA government website? I see it says that a temporary permit is sufficient to apply for a TRN – in the past this wasn't the case so it may be a relatively recent change. I've been doing a bit of reading up online, and it sounds like even some government employees at the licencing department aren't aware of this, so they may try to turn you away regardless. In case that happens, I'd recommend having a printout of the webpage listing the requirements and pointing out that a temporary permit is supposed to be sufficient. You might end up not needing to do that but I find it's always best to be overprepared when dealing with the infamous South African bureaucracy.
Hope this helps.