Most fo the people wish to visit Rajasthan in winter ( from October to March ), as climate is just perfect to bask in the sun and pleasant stay in the night at your comfortable hotels. This time you can enjoy during the day time outdoor activities like camel and elephant safari, witness the fairs and festivals, Go shopping for colorful fabrics, ethnic jewelry, spices with intricate designs and traditional handicrafts.
Temperature in winter may be different part of Rajasthan but in general you may consider in the night it may be around 2 - 10 D Celsius and Day time it may be 10 - 25 D Celsius. Due to desert geographical condition nights will be cooler and days will be sunny and warm enough.
Monsoon season considered in Rajasthan - India from end of June to Mid September but is couple of past years this is very much unusual. You may have rains during the night and day but not too much. It will be very much enjoyable to have your city tour and Camel rides with rain. Honeymoon couple may think about this. There is no precautions to visit during the monsoon in Rajasthan.
Summers in Rajasthan can be considered from End of April Till end of June when temperature may be minimum 25 D Celsius to 45 D Selsius. May and June are the hottest month to travel in Rajasthan. You can avoid hanging out in the afternoon however your visit / City tour in the morning and afternoon will be comfortable. Visiting Mt Abu which is the most preferable hill station in Rajasthan - Udaipur situated in the bank of Lake Pichola and Fatehsagar Lake + Swaroop sagar lake will be interesting. Combine Pushkar for your stay and camel ride and further drive to will take you to Jaipur.