Cold-blooded species from the tropics are intelligently designed to live in the tropics. So, living there is not too hot for them. Plus, many cold-blooded species have the adaptation to take advantage of their warm ambient temperatures, basking in the sun to raise their metabolisms, making it possible to be a lot more active and more successful as a species. Even some sharks and I believe large tuna are slightly warm-blooded, giving them the same advantages.
Here in Northern California, newts can be found under garden rocks, surviving well even though their bodies feel very cold (they hunt at night). Where I live alligator lizards bask in summer, and hibernate from Fall to Spring.
The problem with your ig's eye may be greater than we think. If the bleeding was from behind the eye, it can build up pressure on the eyeball. This routinely causes blindness. The treatment for it is to snip the eyelid vertically over the center of the eye, letting the eyeball pop out as much as it needs to, which stops the pressure on it. That requires lots of nursing to keep it from drying. This is of course an advanced/emergency procedure even in human hospitals. But no vet wants to face the problem of sewing the tiny lid together again. It would have to be done with 20-power magnification. But don't worry, one-eyed iguanas get along well, as do three-legged and tail-less ones. And probably tilted ones too if they don't have continuous vertigo. IMO you should bring this up on your next vet/doctor visit. But it may be too late now.
I really hope your ig heals well. Don't worry that he is not eating. In a week or two, you will have to start syringing water to him. For a passive ig, it would be easy.
Keep in mind that iguanas are very slow to heal. I had a pet iguana who wouldn't eat for a year after a huge peritonitis and sepsis surgery. I kept patiently offering food, syringing water, and also syringed food to her every day. Then one day, two hundred days after the surgery, bam, she dove onto her plate of food and chomped away. That was a great day.