I have a 5570 that horrible about that problem. The screen around the front of the tractor is open in a half-dozen places, so the debris can get into the face of the radiator and oil cooler. This is the only tractor I've ever had or seen that is so designed. Everything else I've seen is set up to stop the debris before it gets to the radiator. I assume they don't have weed and seed stuff in India.
I took some duct tape and taped up the gaps around the hood and the headlights, then shot some spray foam where the side panels and front screen meet. Basically to seal up the front of the tractor where the air has to go through the grill before it gets to the radiator. It looks pretty janky, but it made a huge difference in how hot the tractor gets when running it in those conditions. I used to have shut down every 3-4 hours, come home, open the hood, lower the grill guard, unplug the lights, take off the grill, and clean the radiator. Now it an every two or three days chore. When I'm running the tractor, every hour or so I just wipe the grill off with my hand. Makes a big difference.
I intend to get some weather stripping and maybe silicone and make a better looking fix on it this winter.