It is human body’s response to some inflammation, or irritation in the throat. The underlying causes are varied.
You may cough dryly due to climate change building up in your constitution (physical body). The air-conditioning process may dry up the air movement and the respiratory (breathing) ways too. On entering a building, rapid change of temperature may create a problem, with humidity added.

Chronic coughing, sneezing, and a running nose (cold effect) may result. Avoid cold drinks and fridge food in a climate-controlled room. They interfere with your body heat, and maintenance of temperature physically. Eat hot foods / liquids.
The mucus membrane (nose) has to be pacified and your throat needs to be moisturized, in a warm climate. For dry coughs, inhaling steam from a pan of (Nilgiri) oil may bring relief.