Hi Apoorv and thanks for contacting us. Indian Stars are beautiful tortoises and as far as I can see their temperature should range from 27C - 32C (but not much higher than 32C. Here is a care sheet for them: http://www.reptilesmagazine.com/Care-Sh ... -Tortoise/
but I am sure you already have some good ones.
Regarding your enclosure, is it indoors or outdoors? If outdoors then you could try to make a shady area so that the tortoise can get out of the sun, and have a water bowl where he could go to cool down. If it is indoors then is it an open 'tortoise table' type of enclosure or an enclosed 'vivarium' type? If it is an open one then it will be much easier to lower the temperature. If you have a water bowl in the enclosure then refilling it with cold water regularly will help to bring the temperature down, and if you have a soil-based substrate then spraying that lightly with water (you do not want it to be wet -- just slightly damp on the surface) will also help to bring the temperature down (but don't spray the substrate if it is not soil based). You could also give him regular baths in water that is just tepid, and that will help to keep him well hydrated.
If you take him out of the enclosure then there will, as you say, be temperature fluctuations, but of course in the wild they will also have lots of temperature variations (it heats up during the day and cools down at night every day in the wild), so that is normal and should not cause any problems at all. The only problem would come if it were consistently very cold, or if the temperature went above 35C for any length of time. Also it is important that you measure the temperature in the enclosure at the height of the tortoise's shell (not from a thermometer mounted on a wall of the enclosure).
How old is your tortoise? Obviously very small tortoises can overheat more quickly than a larger tortoise, so there would be more concern for its welfare if temperatures were consistently too high.
I hope that helps a bit. If you would like to send us a photo of your enclosure we could maybe think of small things you could do to keep your tortoise from overheating.