Monsoon is only one of six seasons in Bangladesh. The following is how I would describe the seasons in Dhaka.
Spring (wear yellow on February 13 to mark spring!): February 13-April 14 (20-30 C = 70s and 80s F; humidity is 60 %) or “Hot with Mosquitoes and Why Am I Sweating in February?! Oh, Because It Is 90 F!”
Summer: April 14-June 15 (30-45 C = 90s and 100s F; humidity is 85 %) or “Hotter with Mosquitoes and Constant possibilities of Heat Stroke.”
Monsoon/Rainy Season: June 15-August 15 (30-40 C = 90s F; humidity is 95 %) or “Too Wet, Sweaty, and Hot for Hordes of Mosquitoes-Oddly Not As Hot As It Was.”
Autumn/Fall: August 15-October 15 (30-40 C = 90s F; humidity is 90 %) or “Hot and Dengue Mosquito Season.”
After-Autumn/Late-Fall: October 15-December 15 (20-30 C = 70s and 80s F; humidity is 80 %) or “Hot with Mosquitoes But It Is Almost Wedding Season.”
Winter: December 15-February 12 (15-30 C = 60s and up to the 90s F; humidity is 60 %) or “Wedding Season.” Which is still mosquito season.
As the national costumes remain the same all year round, the men wear lungis and women wear sarees and shalwar kameeses, but in winter, they wrap a cloth like a shawl and a head wrap around their head. To a Bangladeshi 20 C is cold and in the winter when the temperature can drop to 10 C, there are deaths. The Bangladeshis also find warm weather pleasant since they are used to it. Most houses and apartments do not have heating and many have only one air conditioning unit.
In my experience of two monsoons, I have been surprised. In 2012, there was no monsoon. And in 2013, it has rained but not in the torrents that I expected. I have seen worse rain storms in Kuala Lumpur and Washington, DC.
The prevailing theme (you may have noticed) is that all throughout the year, there are mosquitoes and on any day, it can be 90 degrees! I have had heat stroke in December, February, and March, perhaps because I did not expect such hot weather in those months. The result has been a rather silly collection of sun hats.