Map from Google - Bhutan

In Bhutan, the climate is influenced by altitude: it's subtropical in the lowlands, and becomes progressively colder as you climb the slopes of the Himalayas. In addition, the climate is influenced by the summer monsoon, which brings rains and widespread cloudiness for almost half a year.

In the thin flat southern region, in cities like Gelephu and Phuentsholing, the climate is subtropical, with a very mild winter, when the night minima are around 50 °F in January, and the maxima around 73/75 °F; a hot spring from March to May, with afternoon thunderstorms becoming more frequent; and a monsoon season from June to mid-October, with abundant rainfall, sometimes torrential, enhanced by the proximity of the mountains. In winter, sometimes it can get cold at night, while in April and May highs can reach 105 °F. The total annual rainfall can exceed 120 inches. Here, the best time goes from November to February.
Here are the average temperatures of Gelephu.
Average temperatures - Gelephu
Min (°F)505459687275777775705952
Max (°F)737784909088888888868177

In hilly and mountainous areas up to 5,000 feet, the climate becomes progressively milder, with relatively cold and dry winters, and warm and rainy summers, during which the monsoon rains occur in the southern side, while in some inland valleys the summer rains, although present, become less intense. For example, in Punakha, located at 4,300 feet, the average goes from 52.5 °F in January, to 75 °F in July, so the summer is hot and humid despite the altitude.
Average temperatures - Punakha
Min (°F)414652576368686868615043
Max (°F)636672778184828281797368

Above 6,500 feet, winter begins to be cold, with nights usually below freezing. In the capital, Thimphu, located in a valley, at an altitude varying between 7,200 and 8,500 feet, the average temperature goes from 41 °F in January to 68 °F in the period from June to August. Winter is dry and sunny, but sometimes snow can fall. In summer, the monsoon rains are plentiful, so much so that 55 in of rain fall in a year, of which more than 10 inches per month from June to August, and 14.5 inches in July. In the nearby city of Paro, a similar climate is found.
Average temperatures - Thimphu
Min (°F)273439455559596159504130
Max (°F)545761687375777773726459

In some inland valleys like that of Jakar, at 8,200 feet, the monsoon penetrates with more difficulty, so that the annual precipitation is smaller, and stops to 29.5 inches per year, but still with a winter minimum and a summer maximum.
Above 9,200 feet, the daily average temperature in January drops around freezing, and even summer nights begin to be cold.
Glaciers and snowfields begin at high altitudes, above 16,400 feet. In the northernmost areas, the summer rains are not very heavy, but the sky in summer is often cloudy, and you can find mists, or rather clouds lying over the mountain slopes.
The highest peak of Bhutan is Gangkhar Puensum, 24,836 feet high.

Temple in Bhutan

When to go

The best times to visit the mountainous part of Bhutan are spring and autumn, and particularly March and April, and from mid-October to mid-November. During the summer, the rains can make the roads muddy, so it becomes difficult to travel, and besides the clouds can hide the mountain peaks. In winter, the weather is generally good, but it's cold in the mountains, besides snow can fall at high altitudes, and it can also block some passes.

What to pack

In winter: for the plain, spring/autumn clothes, light for the day, a jacket and a sweater for the evening. For Punakha and around 5,000 feet, spring/autumn clothes for the day, warm for the evening, jacket, hat, scarf, sunglasses, sunscreen. For Thimphu and above 6,500 feet, warm clothes for the evening, but during the day a fleece and a light jacket may be sufficient; hiking shoes. At high altitudes, cold weather clothing, synthetic thermal long underwear, fleece, parka, wind jacket, warm boots.

In summer: for the plain, lightweight clothing of natural fiber, light raincoat or umbrella. For Punakha and around 5,000 feet, light clothing, a sweatshirt for the evening, raincoat or umbrella. For Thimphu and above 6,500 feet, spring/autumn clothes, light for the day, sweater and jacket for the evening. At higher altitudes, warm jacket, down jacket, hat, gloves, scarf. For overnight stays outdoors, sleeping bag, warm jacket.