It depends on the caustic concentraction and temperature. For hot concentrated caustics (hot means above 80 ºCelsius and concentrated means above 25%) the only metals that resist corrosion are silver and nickel. Lining of vessels subject to those conditions (caustic soda evaporators, for example) is made with pure nickel, a very expensive metal, although cheaper than silver.
If your only concern is PWHT because your conditions are not so severe, then instead of Inconel, another quite expensive alloy, you may use an L type stainless steel (AISI 316L for example) with a carbon content of 0,03% maximum, which precludes the danger of intergranular corrosion, or a stabilized type stainless steel (AISI 316 Cb for example), which contains columbium (also called niobium) that will combine with carbon and leave the chromium intact.
Giovanni S. Crisi
Sao Paulo - Brazil

I'm don't know the ins and outs of your particular corrosion situation, but metallurgically, inconel 182 is metallurgically very compatible with both overlaying carbon steel and PWHT. However, Mr.Crisi hit it on the nose if you are looking for other alternatives. (309L, and Nb stablized sst are subjected to PWHT quite frequently.)