Advice for 5 weeks in India - Rajasthan and/or Kerala

Hi I am currently travelling in India for 5 weeks or so with my girlfriend and our travel plans are under review in light of our naivete about Indian climate! Basically we are currently in Uttarkhand and enjoying the relative coolness of the northern states - seeing Mussoorie, Dharamsala and Amritsar etc.

The trouble is that we had planned to go south through rajasthan to mumbai, and then down past goa to kerala, then getting a train from chennai or bangalore back to delhi to fly on the 1st of july. Having done a bit of research we are worried that rajasthan will be far too hot, (we found Delhi's heat quite exhausting, though we are adjusting little by little) and that the monsoon in Kerala will make travel and relaxation much more difficult.

We are fairly relaxed people and would ideally like to minimise times in cities and hectic locations and are instead interested in sampling more relaxed indian culture and natural beauty.

Basically, we cannot decide whether to continue with all or part of our original plans or concentrate more on the north, perhaps venturing further north in uttarkhand and maybe seeing the valley of flowers of doing a trek.

Will rajasthan be far too hot for us or will it become cooler in mid-june, and will the rains in kerala be unpleasant or even dangerous to travellers?

Sorry for the long-winded message, any advice would be greatly appreciated.

If you don't like the heat, head north through Manali to Leh. Maybe spend a couple of weeks in Rajasthan at the end. By the end of June it might cool down a bit.