Some important factors affecting the flatness of bread are:
Some grains aren't suitable for thick breads. Barley breads, oat breads, lentil breads, etc. are usually flatbreads. Non-flatbreads are usually wheat or rye.
Availability of ovens. Both home ovens and commercial ovens can be important. While many flatbreads are cooked in ovens, there are many alternative cooking methods, such as frying, grilling, roasting, baking in ashes. For non-flat breads, over-baking is the most common method. Steaming is another method that can used, but is usually restricted to small breads (bun-sized rather than loaf-sized). Homes in warm climates were often traditionally without ovens. Nomadism also discourages oven-ownership.
Availability of large-scale milling. If grain (or pulses like lentils and chickpeas) are milled by hand into flour, as a daily task in the home, bread will often be made in small batches, daily. Large-scale milling allows mass-production of bread, taking advantage of economies of scale by using large ovens.
Non-flat breads are common in many hot regions. Sometimes, such non-flat breads are much more common in urban areas, where bread is commonly made commercially, compared with rural areas where bread is more likely to be made at home. Thicker flatbreads, which are often best baked in ovens, also benefit from commercial baking (sometimes, the bread was traditionally made at home, and baked in a shared village oven).
Thus, two important factors will make flatbreads more common in warm climates: low urbanisation, and lack of home ovens. Bread will be made with home-ground grain, and cooked daily. Lack of home ovens partly results from warm climates, but low urbanisation is a largely historical contingency, due to the earlier urbanisation and industrialisation of Europe.
Another factor affecting bread in general is the importance of bread in the diet. Where other staples are eaten instead of bread (potatoes, yams, rice, pasta/noodles), bread can be of relatively minor importance. Thus, urbanisation in Japan didn't give rise to a significant bread culture until after WWII (today, toast and coffee is a common Japanese breakfast), but instead resulted in a much greater consumption of white rice (and less barley and other grains). The potato reduced the importance of bread in many parts of Europe, including some regions with fairly low urbanisation.
Many of these factors come together to make South Asia a region where flatbread is very common (even though rice does reduce the dependence on bread in many areas). Home-made bread is usually flatbread, made with wheat or sorghum/millet or pulse flours, and is often fried on a griddle (and sometimes deep-fried). South Asia bread traditions overlap with Central Asian and Western Asia bread traditions, where oven-baked thick flatbreads (usually called nan or naan or non; these are usually baked in a tandoor or tandyr oven) are common. In India, home tandoor ovens were traditionally rare, but women would often take their bread to a communal tandoor to be baked (and the social interaction about the oven was an important part of village life). As communal ovens have disappeared, commercial bakeries will provide the same baking service. Otherwise, tandoor-baked breads are available commercially.
In Central Asia, many rural homes have tandyr ovens, but earlier, communal ovens were common (and tandyrs are being replaced by modern in-home ovens in some regions). Commercial bakers supply bread in urban areas. Some examples of ovens and cooking bread:
Tandyr nan (often considered the thickest type of flatbread) for sale in Kyrgyzstan: https://commons.wikimedia.org/wiki/File:%D0%A2%D0%B0%D0%BD%D0%B4%D1%8B%D1%80%D0%BD%D1%8B%D0%B5_%D0%BB%D0%B5%D0%BF%D1%91%D1%88%D0%BA%D0%B8_%D0%BD%D0%B0_%D1%80%D1%8B%D0%BD%D0%BA%D0%B5_(2).jpg
Cooking bread in a communal tandyr, in northern Iran: https://commons.wikimedia.org/wiki/File:Baking_bread_by_nomad_women_in_Lar_National_Park.jpg
Cooking filled buns (as street food) in a tandoor in China: https://youtu.be/RUGNrv596O8?t=33
Baking in a tandoor in Afghanistan: https://youtu.be/ZNCoKdZUw6M?t=261
As said already, there are many common cooking methods other than ovens. For example, commercial breadmaking using a griddle:
On to Europe! Northern Europe, with many home ovens, and old bread traditions often based on commercial milling and large-scale baking, features mostly non-flat breads. However, flatbreads are not absent. Some traditional flatbreads have become scarce (probably because potatoes replaced oat and barley flatbreads in the diet in many cases), but some flatbreads continue to be common in modern times. Oat and barley flatbreads are still made as traditional foods in Ireland and Scotland, and elsewhere in Britain. These were often fried on stone griddles, or roasted beside the fire; today they are often oven-baked. Flatbreads remained the common breads in many parts of northern Europe into modern times, due to lack of ovens. For example, flatbread (podpłomyk) was usual in rural Poland well into the 19th century because poor homes had no ovens.
The Nordic region, in particular, has a strong and continuing flatbread tradition. In many Nordic regions, flatbreads were the most common bread into modern times, while in other places, they competed with loaves of rye bread. Some Nordic examples of flatbread:
Thin and crispy Norwegian flatbread, a traditional peasant staple: https://commons.wikimedia.org/wiki/File:Br%C3%B8dkorg.JPG
A soft Norwegian flatbread, lefse, often eaten rolled up: https://commons.wikimedia.org/wiki/File:Rakfisk.jpg
A selection of Finnish flatbreads, including rye crispbread, soft rye flatbreads, and the large rye flatbread with a hole in it for storing on poles, reikäleipä ("hole bread"): https://commons.wikimedia.org/wiki/File:Ostrobothnian_house_interior_with_rye_bread_drying_on_a_pole.jpg
Two types of Swedish crispbread: https://commons.wikimedia.org/wiki/File:Tunnbr%C3%B6d-2007-07-14.jpg
Traditional Icelandic bread was usually flatbread into the 18th century, when rye sourdough loaves, often cooked by steaming on the stovetop, covered by an upside-down pot. The older flatbread commonly used seaweeds and the seeds of wild grasses to stretch the supply of grain.
On to China! Northern China - certainly capable of seriously cold weather - has traditionally depended on wheat as the staple. Much of this was eaten as noodles, but breads also appeared. A wide range of fried flatbreads, sometimes stuffed, were (and still are) eaten:
Fried flatbread (bing) from Shanxi province, China: https://commons.wikimedia.org/wiki/File:Bing_zi_(Chinese_pancakes).jpg
Lao bing, a thin fried pancake: https://commons.wikimedia.org/wiki/File:Lao_bing.jpg
The pancakes made famous as the wrapper for Peking duck: https://commons.wikimedia.org/wiki/File:Peking_Duck_1.jpg (with duck in background).
In addition to these flatbreads, there are also steamed breads, sometimes filled:
The use of steaming and frying results from a lack of home ovens. While stoves were important for keeping warm in winter, a common arrangement was a hole (to hold a cooking pot, e.g., a wok) directly over the fire, and suited for baking. (Heating was often achieved by channeling the hot exhaust under the floor of the living quarters, either heating the whole floor or just a sleeping area - this type of system was usually called kang in Mandarin, and ondol in Korean. In summer, the hot gas was just vented directly to the outside.)