Question: Given an Earth-like planet, what sort of geological features or weather systems are required for a place to have the same average day and night temperatures throughout the whole year? Is such a thing even possible?

The closest I could think of were tropical climates that are hot all year long (though even these have cooler wet seasons), but I'm looking for something more temperate, around 15-25°C during the day.

The minimum area of the region should be roughly as big as Belgium.

Answer: 
It's called a cave. Go down about a hundred feet and the weather pattern is very stable. It's a bit chilly, but not impossible to make a comfy place.

Avernum takes place in a giant interconnected cave system.

The same could be said for the Underdark, though I've only been there in Neverwinter Nights so I can't say if there are storms.

Journey to the Center of the World also featured interconnected cave systems.

If you want something a little more open, a Dyson Sphere or Ring should also have the same temperament everywhere unless something's gone terribly wrong. Like the heat source drifting closer to one wall (floor?) than another.

Planets can't really be temperament unless they're tidal locked to their star. Then it's all about placement. The side that's locked toward the star would be hot, then a safe zone around the Dawn Belt and finally a frozen wasteland on the other side. Our moon is Tidal Locked to the Earth meaning that for millions of years, we've only seen one side of her.

If you have a dimensional disturbance story (a.k.a magic) or a possible Fey Loci then that would solve the problem as well.
This may not be the answer you are looking for, but thought I'd post it anyway: if a country is close to the equator (e.g. Sri Lanka), the temperature would be same (approx. 30 degrees C) all year around. The day time is also fairly constant i.e. sun rises at about 6am and sets at about 6pm (variation through the year may be about 1 hour).