The world has been how you describe (ocean at both poles) for most of its geological history, with fossils providing quite good evidence for its climate over the last 500My or so. We can therefore answer the question of how it would be in one word: warmer! Think steaming tropics too hot for any but very small mammals to survive (but good for very large crocodiles), and a Mediterranean climate close to the poles. Probably also large expanses of desert too hot for any life at all (like Death Valley warmed up a bit). Precise details of climate and ocean circulation are of course determined by the configuration of continents as well as the absence of ice. Which configuration is quite markedly changed by a 200ft rise in sea-level -- say goodbye to Florida and most of the Missisippi basin, for starters.
There is a positive feedback loop and a lock-in effect. The positive feedback is that ice is highly reflective. The more ice, the more sunlight is immediately reflected straight back into space. So advancing ice causes global cooling leading to an ice age, and retreating ice causes global warming leading to more ice melting. (Throw in methane clathrates melting as the ice covering them melts, and there's a good chance of methane-induced run-away global warming over mere centuries). The lock-in is that once all the ice is gone, there's nothing feeing freezing cold water into the oceans, and the huge reserve of cold 4C water at the bottom of the oceans starts to warm up. Over a few tens of millions of years, the ocean becomes a pretty huge reservoir of warmth.
So why won't the human race stop burning stuff? We may already have put ourselves on a one-way trip to a planet with sea-level 200 feet higer, and at least four-fifths of the remaining land area uninhabitably hot or humid.
If you think that's pessimistic: this planet is very close to the inner edge of Sol's "Goldilocks zone". The real ultra-pessimists think, maybe not inside it at all any more (the sun is gradually getting hotter as it ages), so that once all the ice melts, the global warming effect of all the extra water vapour in the atmosphere will overwhelm the added cooling caused by increased cloud cover, and the planet will end up as a cooler version of Venus.