They'll probably be extinct for other reasons, before climate change has a chance to wipe them out.
Remember, an increase in temperature will have a corresponding effect on the oxygen-carrying capacity of blood (and water) (reducing it). Cold-water species will not necessarily grow faster - they will more likely be forced into and restricted to areas of relictual cold water at extreme high latitudes.
Think also of the sperm whale - the bull migrating to high latitudes (very cold water) to dine on megasquid. If these cold waters vanish (due to global warming) then we'll lose a major component of the diet of these whales. If warm water was so condusive to growing 'large/mega' squid, why is it that these beasts are today limited to cold waters? There's more to this that simple temperature; if temperature was all it was about then we'd have the largest squid species in the tropics.
Many cephalopod species are unlikely to be able to tolerate increased temperature (high latitude or deep-sea); increased temperatures will only benefit those species tolerant of increased temperature; cold-water species will simply vanish.
I've also been reading that all the massive melting going on in polar climes will ultimately end up lowering salinity levels which would be devastating for a lot of ocean life. The reasoning behind the threatened extinction of polar bears is that their primary habitat is vanishing; these are creatures that are evolved to hunt on pack ice.
Incidentally, with that much polar ice melting and entering temperate seas, shouldn't this actually lower the water temperature by some degree? Like when you melt ice cubes in a room temperature liquid, it ends up lowering the total temperature. The influx of that much cooler water ought to have a detrimental effect on some of the major current systems. Also, as the cooler water temperatures meet more equatorial zones, won't this produce more - how should I say this - "dramatic" weather?
Global periods of warming and cooling have always been a natural, cyclical process. What has many of the planet's climatologists concerned is the fact that it appears to be happening at an accelerated rate. Mind you, in certain quarters this is still highly controversial. All I know is our weather here in S. California has definitely been getting wetter lately, and in the Southeast part of the country there have been more tropical storms and hurricanes per season recently. It may come to the point where the good citizens of New Orleans will have to tow Chef Paul Prudhomme out to block incoming storm surges with his body to save the Crescent City!
The most dramatic effect of melting ice sheets will be indeed the lowering salinity, hence water density in n.Atlantic for instance and as a consequence will most certainly stop the conveyor belt process (transporting salt out of the N.Atlantic and heat into it) known as the thermohaline circulation. This will have a detrimental effect on current weather patterns, marine, terrestrial organisms.
Quick bit of gene sequencing and we can cross breed the giant squid with the polar bear and make a furred, tentacled predator that is not bothered when the pack ice vanishes, capable of pursuing seals on both sea and land, and underwater. Also would make a tasty dish for bull sperm whales!
Seriously though, are there likely to be undiscovered, very large squid in the Arctic Ocean, or are they mainly an Antarctic thing?