I ran 2 MSI TWIN FROZR OC HD 7980's until 2020 when I started to do a core component upgrade from my MSI 970 Carbon Elite MOBO to an MSI X370 M7 ACK MOBO.
Even in crossfire the 8GB of VRAM was starting to struggle on newer games.
Never had heat issues.
Then Windows 10 would not run games unless I ran in compatibility mode for windows 7.
I purchased 2 RX 590's about 2 months before the GPU market prices went into geo sync orbit.
I guess what I'm saying is even if you do repair the GPU the load placed on it in gaming is going to be heavy.
I suggest running at a resolution of 1024x768 or 1360x768 with a capped refresh rate of 60Hz to reduce load and heat generation on your GPU.
Keep an eye on trusted online sites like Amazon Newegg and Best Buy for weekend sales and sales following major holidays. Look for RX 580's RX 5700 or 5800 XT's maybe even 6600 6700 6800 series. You never know when a sale is gonna save you $500 to $1200.
Oh and look for the GPU's with dual fans and multi heat pipes to keep it cool. Those single fan GPU's just don't cool effectively honestly they never have.
You could try to find a high end aftermarket dual fan GPU cooler that's compatible with your GPU that may keep it running till you can upgrade.