Hi Wolfie, Broadly this is correct but it is more involved, to keep it simple there are two methods of case hardening, both involve “putting” a skin of carbon steel on the outside of a low carbon [mild] steel.
The simple one for small parts requiering a thin skin say 0.002″ to0.005″ is to use a prepared compound from I understand, Blackgates or Chronos [Used to be Kasenit] and a good sized gas torch, heat the work to red heat and dip in the compound–it should stick to the hot metal, might need to dip again to get enough on the work. Then heat in the torch for several minutes and quench in water. You will now have a hard case. You will rarely need to temper with this process. What you have done is add carbon to the surface layer thus enableing it to harden, the core will remain soft.
With this method there are considerations due to holding the steel at elevated temperatures for long periods which give rise to grain growth in the core which weakens the material–it can be overcome by secondary treatments–see the link.