I also thought about wet bulb and checked the humidity in Delhi, which seems to be just 7 % or so. According to wet bulb calculators that's still good, like around 23 °C wet bulb.

Interestingly the wet bulb temperature calculators that I tried only work until 50 °C, so that was what I put in.

At 50 °C you need about 35 % humidity to get to 35 °C wet bulb.

Regarding your second point: If I'm not mistaken, the hottest month in the region is around May. The temperature is influenced by monsoons, and although the sun peaks higher in summer, it is generally also more cloudy and rain cools of the surface. That's why usually temperatures peak just before rain season.