Hello and welcome to the forum!
Rajasthan can actually be visited all throughout the year. But like you said, summers (April to June) can get extremely hot here. May to June are considered the hottest months in Rajasthan. If you're from a country that's cold, you might get uncomfortable if you're visiting Rajasthan during these months. Your best option would be to visit the Mount Abu, which is a hill station in Rajasthan. During the summer months, it's a bit cooler here and you have lots of attractions to visit as well.
July to September is considered as the monsoon season in Rajasthan. From July to September, you might experience hotness and humidity in Rajasthan. However, visiting Udaipur during these months is great as the place comes alive with all its lakes. Monsoon showers can be seen sometimes here and it transforms the landscapes of Rajasthan, especially the Thar Desert. You can also witness many festivals during these months. Rates are lower as it isn't peak season as well.
Lastly, from October to March, this is considered the winter season in Rajasthan. During December to January, temperatures can drop as low as 0°C and even below. These are actually the best months to visit Rajasthan as the weather is cooler and you can explore the desert, city and other places quite comfortably. Since this is also the season when tourists flock to Rajasthan, there's lots of activities going on during this time. There's the Bikaner Camel Festival during January and the Desert Festival during February. You can visit any place in Rajasthan during this time as well.
I hope this helps!
