Well, in order for the sun to quickly melt the polar ice caps, it would have to burn so hot that it would most likely kill everything on the planet. The oceans would boil.

But, I understand what you're asking anyway. You're asking that if suddenly the polar ice caps began to dissolve into the ocean, would that have a lasting effect on the world's entire climate? Most certainly. I have no idea exactly what that would do (besides causing massive oceanic rises and worldwide flooding), but it would absolutely cause permanent changes to the entire planet's climate.

But do you understand the point I've been making? There's absolutely, positively no way for something like that to happen without causing death to the entire planet. The ice caps can't just melt in a matter of days, because the heat required to do so would kill everything on the planet. Climate changes don't happen in a matter of days. If one did, we wouldn't survive it. It wouldn't be a "climate change", it would be "the end of the world."