When I sweat in summers, am I losing calories?

No. Sweating in summers is a mechanism to dissipate excess heat. It results in loss of water and some electrolytes (sodium, potassium and chloride) from skin. The final effect is cooling.

When someone exercises, there is sweating too, but the loss of calories occurs primarily due to exercise, and not due to sweat.

So don't think that if you're sweating, you're losing calories. Standing still in heat won't help you in losing calories. To lose calories, you'll have to sweat it out in the gym!