Harden of simple steels is possible with a forge. Most simple steels reach their critical temperature around 1500f. Big clue is a magnet will not stick to them after about 1450. A few shade lighter red and your there. Guys who do good HT this way use a low light in the forge area to recognize the right color consistently. If you polish hardened steel and heat you can recognize the lower temps by color. Straw is around 400. But, this does not give the best temperature as a good temper needs time for the structure of the hardened steel to fully temper. 2 2 hr cycles at 400-450 is best. If you want a very hard edge that will never be banged on hard material 400, if it will be abused 450. The harder it is the more prone to edge chipping the softer it is less likely to chip, but starts to get edge roll over if to soft. But a kitchen oven or a good well regulated toaster oven does a good job of this. High carbon steel hardened in an oven or forge will have a very thin layer of steel on the outside that has lost some carbon. This needs sanded off. Sometimes people file a piece after its hardened and the file bites a bit. This doesn't always mean the steel is soft. Just a bit on the outside is decarbonized. A few thousands in it can be fully hardened.

Stainless steels are very poor candidates for hardening in a forge. It can be done, but never real well. The high amounts of chrome make itt more difficult for the carbon to get in full saturation. Most stainless steels call for a temperature of around 1850f or more and about a 30 min soak time at that temperature. Very difficult to hold a consistent 1850 with a forge for that long. Plus at that temperature the steel will lose a bunch of carbon on the outer areas very quickly. I HT stainless steels in a envelope formed from 309 stainless foil. This keeps the oxygen away from the steel so it does not burn of any carbon.