WARSAW, Poland — Nearby the big city rumbles, but one feels almost transported to a quiet forest village when standing amid a colony of Finnish wooden houses in Warsaw’s government district.

The homes, erected as temporary housing in the destroyed capital just after World War II, have dwindled over the years from 90 to about 25. Now the surviving structures have become a point of contention between their inhabitants and a city government keen on tearing them down to make way for new developments.

It’s a story being played out in various ways in Warsaw these days, as the Polish capital undergoes a building boom that makes new constructions lucrative for developers and attractive to city officials eager to put their mark on the city. But such change often comes at the cost of old buildings of historical or sentimental value to others....