

The question of how to cool shit in space is something that BioWare asked themselves when writing the Mass Effect series, and they came up with some pretty detailed answers that they put in the gameās Codex (āStarships: Heat Managementā in the Secondary section, if youāre looking for it).
That was for a series of sci-fi RPGs which havenāt had a new installment since 2017, and yet nobodyās bothering to even ask these questions when discussing technological proposals which could very well cost billions of dollars.

I know youāre joking, but I ended up quickly skimming Wikipedia to determine the viability of this (assuming the metal heatsinks were copper, since copperās great for handling heat). Far as I can tell:
The sun isnāt hot enough or big enough to fuse anything heavier than hydrogen, so the copperās gonna be doing jack shit when it gets dumped into the core
Fusing elements heavier than iron loses you energy rather than gaining it, and copperās a heavier element than iron (atomic number of 29, compared to ironās 26), so the copper undergoing fusion is a bad thing
The conditions necessary for fusing copper into anything else only happen during a supernova (i.e. the star is literally exploding)
So, this ideaās fucked from the outset. Does make me wonder if dumping enough metal into a large enough star (e.g. a dyson sphere collapsing into a supermassive star) could kick off a supernova, but thatās a question for another day.