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.
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).