How can I see the operating temperature of my iPhone?

I don't know of an tools that will do that on an un-jailbroken phone. I would suggest you post in one of the developer forums. I think you're more likely to find what you need there. Either people can recommend tools or weigh on on the feasibility.

My personal opinion is that this sounds like a really bad idea. iPhones are consumer devices and not really intended to be used in extreme conditions. As an example, I looked up the the tech specs for the iPhone 14:

Operating ambient temperature: 32° to 95° F (0° to 35° C)

Nonoperating temperature: −4° to 113° F (−20° to 45° C)

Relative humidity: 5% to 95% noncondensing

Operating altitude: tested up to 10,000 feet (3000 m)

I suspect your client will have no end of trouble with this no matter what you do. But, I wish you the best of luck.

[Edited by Moderator]

If the phone gets too hot, you will see a warning on the screen and the phone will turn off.