by buildings temples of the lost, you can essentially guarntee that academy contests are going to be influence based (cause they are somehow determined by which resource is produced the most) this in turn means that by doubling down on templest of the lost, you obtain a massive advantage in any academy contest to come.

Temples also fuel your influence spheres and of course the associated system to academy conversion which in turn means more relics.

The tallest play you can do is build the faction unique building that scales per temple, so you basically get one supersystem.

You assign relics to heroes on hero screen https://youtu.be/bHwGTDmePHY?t=2156 

And relics to empire to on empire screen. https://youtu.be/bHwGTDmePHY?t=2141

It's -50% FIDSI from basic planet output, not from System. It's not as bad as it seems, thought I hasitate to build it on systems that don't benefit from increased influence zone.

You cal also spam temples by default on cold planets, since they don't give you much else.