When flying from Hyderabad to Monterrey, the time of day you decide to fly out makes little to no difference towards the overall price you’ll pay on tickets.
When travelling, it's generally smart to pack in preparation for rain or any other conditions that may arise. The rainfall in Hyderabad is roughly greater than that of Monterrey. You can assume this to be the case over the next 6 days.
Expect the weather to be around 39 °C on average in May. As the temperature peaks, try to get your plans done early, as flight price and availability will have an impact on your travels. The climate in Monterrey is generally colder than in Hyderabad.