No they dont if their warranty T&C says warranty is void if you remove the cooler then nothing you can do about it they dont have to prove anything.
Rubbish - T&Cs cannot override consumer legislation. This would be similar to having a warranty claim denied for the suspension on your car because you changed the air filter. The consumer rights act states that goods must "of satisfactory quality", which also includes an aspect of durability. It wouldn't be difficult to argue that a premium £1k+ flagship GPU should last more than 12 months
under normal use, particularly when most manufacturers offer 2, 3 or even 5 years warranty on the same product.
Of course the bold part is critical - if they can prove that it
did fail due to overheating because the cooler wasn't installed properly, or provided insufficient cooling (which is perfectly plausible), then they are perfectly correct to decline the claim as it failed due to misuse, NOT due to a manufacturing/design fault.
However, this then comes down to how it was sold by SB Computers - if this was a standard configuration they offered, determined to be appropriate by a trained professional and there was no warning to you that this would void the warranty, then in my opinion you have a pretty strong case against them - back to the legislation above, you (as a consumer with no technical knowledge) bought a premium product from a knowledgeable business, with the expectation that it would be of satisfactory quality - buying a 2.5k high-end gaming PC from a specialist gives you much higher expectations than a generic £300 Chromebook from a high street electronics warehouse.
If on the other hand you basically gave them a list of parts you wanted and asked them to build it for you, then you will have a much weaker case.
TL;DR
One of 3 things has happened:
1. The card has developed a fault which is unrelated to cooling.
2. The card has developer a fault due to the aftermarket cooler being installed incorrectly.
3. The card has developed a fault due to the aftermarket cooler being insufficient/incompatible.
If it's point 1 then this should go back to the manufacturer, as the fact an aftermarket cooler has been fitted is irrelevant, and it comes down to an expectation of "satisfactory quality", and what should be considered a realistic lifespan for a flagship GPU (refer to the length of warranty provided by other companies)?
If it's point 2 then this is down to the retailer to address as they have failed to provide a product of satisfactory quality.
If it's point 3 then this depends on who specced the card/cooler combination? If it was you, then you are probably a bit screwed tbh, but if it was the retailer, then it's clear it was not fit for purpose and so again it comes down to them to address.
edit: when you realise your TL;DR is actually longer than the post itself
