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: 
A large body of water can have an enormously stabilizing effect on the weather. It is a common joke that weather at San Diego is the same year round.

While not entirely true, it does have some truth to it. Summer in San Diego usually has a range from 65F to 75F, while the Winter range is 50F to 65F. I live at about the same latitude, but several hundred miles inland (and several thousand feet higher) away from any body of water and temperature can range from 63F to 92F in summer and 27F to 53F in winter.

Water does not guarantee a mild climate though, as the Great Lakes region is known for its Lake Effect snow which can drop a substantial amount of precipitation in a short time.
The simplest answer was given above: give the planet a perfectly circular orbit with zero obliquity (no axial tilt) and each part of the planet's surface will receive the same energy from the star year-round. You could take this a step farther and assume your planet is orbiting a red dwarf star such that its habitable zone is close enough that the planet becomes tidally locked to the star, so the planet always shows the same face to the star. This can make the planet look like an eyeball (see here: <https://planetplanet.net/2014/10/07/real-life-sci-fi-world-2-the-hot-eyeball-planet/> or here: <http://nautil.us/blog/forget-earth_likewell-first-find-aliens-on-eyeball-planets>). For an eyeball planet the temperature structure would vary a lot across the planet but not in time.

The thicker the atmosphere, the more uniform the temperature across the planet's surface (Venus is the extreme example, but one to be avoided if you want life on your planet). I don't have a good feeling for the effect of the spin rate on the stability of the local temperature. Faster-spinning planets will have more "banding" structure in their atmospheres but I don't know if that is a stabilizing force. Someone with a specialty in atmospheric dynamics would probably know.