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: 
Seasons are pretty universal, being caused by the angle at which the sun's light hits the planet. To make a point on a planet without seasons, you have two main options:

1. Give the planet's axis no tilt. This will allow you to have different regions with different temperatures depending on their distance to the equator, but no seasons anywhere else on the planet either.
2. Put the planet further away from the sun, so it is cooler overall. The tropics will still be season-less just like on Earth, but their temperature will be cooler.

A planet with an extremely thick atmosphere that blocks out the sun and heats the planet through greenhouse gases will have less temperature variation over the entire planet. Of course, such a planet will not actually be Earth-like.
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.