India - April through July

I will be in India between April and the end of July. I plan to trek in Nepal for a few weeks, but the rest of the time will be spent in India.
I understand that due to weather conditions, I will have to spend most of the time in the mountains. But I would also like to see Varanasi, visit Punjab, Agra.
Would that be possible any time between April and July or is too hot during those months?
When does it get too hot and how far north do I have to go to avoid the heat?

Many thanks!

I think escaping the heat is more a matter of altitude than latitude. So just going north isn't the answer - you have to get off the plains and up into the hills (of course, many hill areas are in the north, so in that sense "going north" can help you beat the heat).

Varanasi and Agra will definitely be hot, hot, hot, but Varanasi is so fascinating (at least to me) that you may just want to brave the heat anyway. Apart from the Taj Mahal and Fathepur Sikri and some other Mughal monuments, Agra didn't really grab me - maybe best to leave it for some other time of year unless you feel that it's a sacrilege to go to India w/o seeing the Taj.

I don't know what your particular interest in seeing the Punjab may be, but can I suggest an alternative (or addition) that's perfect during the time you'll be in India? Ladakh! There's info on other threads about it, and there are also lots of other websites where you can find info. And if you're going to be in the Punjab anyway, you can fly directly to Leh from Chandigarh (at least you used to be able to - I haven't checked the airline websites to confirm this - I highly recommend Jet Airways).