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.
High altitude tropics
=====================

While San Diego has remarkably stable temperatures year round, there are other places that are even more stable. In tropical highlands, places get the same stable insolation as the steamy lowland tropics, but the air temperatures are mitigaged by altitude. This results in basically the most pleasant places on earth.

There are several tropical highlands straddling the equator. Africa has the Rift Valley mountains, from [Ethiopia](https://en.wikipedia.org/wiki/Addis_Ababa#Climate) and [Nairobi](https://en.wikipedia.org/wiki/Nairobi#Climate) in the Kenyan Highlands through [Rwanda](https://en.wikipedia.org/wiki/Kigali#Climate) and Burundi. All the cities in the Andes from [Caracas](https://en.wikipedia.org/wiki/Caracas#Climate) to [La Paz](https://en.wikipedia.org/wiki/La_Paz#Climate) have pretty stable temperatures. And through extraordinarily wet, the [highlands](https://en.wikipedia.org/wiki/Mount_Hagen#Climate) of New Guinea have very stable temperatures too.