First, there are two ways to look at this question
An earth-like planet that becomes a water world.
A world that naturally evolves as a water-world.
Those are important distinctions. An earth-like planet would either need an "explanation for the Biblical flood" solution (e.g., something squeezes all the water from the aquifers type of thing) or a "water was added to the system" type of solution (e.g., an ice asteroid hit the planet bringing enough water to flood it.) Either way, given that things are allowed to "settle down" into their new water-covered state, what would you have?
What you'd have is ice—and a lot of it. From this perspective Minecraft is right. Now you mentioned a rise of only 36 meters from typical. Let's use the seal level simulator from Floodmap.net.
If you set it to 36 meters, you don't have a water world. Most of the landmass is intact. You don't have ice in this scenario as the world hasn't really changed. You'd have a bit more polar ice, but that's about it.
If you set it to 500 meters, you have more of a water world, but there's still a LOT of land. I wouldn't expect ice in this scenario, but people are at measurably higher elevation, so a colder climate would be expected. Your polar ice would be pretty big and global warming would no longer be a problem.
At 1,000 meters I'd claim we have a true water world, but there's still enough land (go look at Greenland, the world's new superpower...) that you could save everyone on Earth today and probably feed them (that's a lot of ocean for fishing...). Except for the ice, which likely covers the earth.
The problem is that simply changing Earth means that you have the normal heating conditions of the sun and what we know of high-elevation temperatures coupled with a higher rate of cooling (a LOT more water in the atmosphere and much more evaporative cooling) and the fact that water is more thermally conductive than dirt. In other words, no more global warming. It would be a permanent ice age with a thriving underwater ecosystem because all that solar energy is still arriving and underwater vents still exist. Thus, I wouldn't predict a thick ice sheet on the ocean, but I would predict all the land covered with ice and substantial ice shelves.
But, what about world #2?
For a moment, let's consider the goldilocks condition for a true water world. In this case the planet is absolutely tropical. It's a bit closer to the sun to balance the cooling effects of the water. There's no ice, anywhere, not even at the poles. What land is exposed is either lush with life or completely barren. I'm going to ignore the analysis of deep-ocean vs. shallow-ocean. That would have a substantial effect on the plant life, but not the average planetary temperature as the orbit would simply be adjusted to balance it out. For fun, we'll assume deep oceans like ours.
That world would be teaming with happy oceanic life. Lost of elbow room.
OK, but what about the weather?
In both circumstances (#1 and #2), you have substantial storms. A TON of water is evaporating into the atmosphere and there's fewer blocks to wind. Ocean currents are still moving around undersea continents, but there's a lot less drama involving them. Which means you have striated currents, striated winds... You'd have a planet with whooping high winds, really BIG storms, and almost constant cloud cover.
An Important Message from Our Sponsor
@FinAndTonic brought up an incredibly good point that throws some of my answer into disarray (but I haven't time tonight to rework it all). As sea levels rise, they push the atmosphere up with them.
Here's the problem: the idea that things are colder at "higher altitudes" is based on thinner atmosphere. We humans ofttimes don't respect just how thin the golden biosphere really is. That two kilometer band above sea level is prime happy land: warm and inviting. Above that things start getting dicey until you reach the "death zone" at 8,000 meters.
But if you add water, the water pushes the atmosphere up. So the death zone is still 8,000 meters above the new sea level.
Now, there is a complication with this: the Earth's mass isn't materially changing with the addition of new water. That means that while we're pushing the atmosphere up, the loss of atmosphere to space increases. At this moment I don't know if that increase is enough to lower the atmospheric density to bring the ice back into play.
But it's uber-cool to think about.