Temporary or event relics work the same way the globals relics do, except they're limited in two ways :
1- They only work in specific locations (can be an event dungeon, LOL, arena and/or gauntlet, etc.)
2- They only work for a set timeframe (7 days, 15 days, etc.)
They often come in big increments (+50%) and limited in number (2 of a kind).
They always require you to either buy them (with gold, ironite or RWC) or earn them (through event specific challenges).
The prices are often steep, so measure your investments.