Yes and no.
The newer iOS devices have internal temperature sensors and will let you know when the internal temperatures are so high that damage is of concern. You basically get locked out of the device until it's cool enough to run again.
As long as the sensor is working, it is safe to use the device up until it shuts itself off. This protection should cover you from charging or operating the device and causing harm to the components in the short term as well as drastic long term damage to the battery.
If you are concerned about the long term health of the battery - then yes, do worry about temperature. At 0°C - you can expect to lose between 2 and 6% of the capacity per year depending on the average charge in the battery (the lower is at 40% average charge - the higher is 100% average charge). If the temperature is 25°C - these losses jump to 4% to 20% capacity loss. If you store/use the phone for one year at 40°C which most people would consider very hot to hold - the losses in capacity are 15% to 40% annually. Charging the battery this hot or hotter is even worse for the health of the battery.
So, a few times of limited use under 40°C shouldn't be of concern, but leaving it in a very hot car (> 50°C) can be very damaging if it's charging or there for hours or days.
Whenever you can keep it cooler, and not fully charged for long periods of time, your battery will degrade less over time. You can weigh the need to use the battery when warm with the eventual replacement cost of $79 if you should ever just need a battery swapped out by Apple.
The answer you are expecting won't satisfy you because the cost of making those devices is much less then the price they sell them for...
But in order to answer your question, I've made a table. Unfortunately, I didn't find any records of the iPod touch 16GB and 32GB, but I expect they are quite alike.
I'm sure Apple does get his share on the sold subsidized iPhones too.
The difference between US and Europe is the difference between a locked iPhone and an unlocked iPhone (because in Belgium, you pay this much for an iPhone...)
Here is an interesting article about the difference in production costs between an iPod touch and an iPhone.
And if you want to know what an iPhone costs in detail (every part), take a look at this overview.
So, although it seems like Apple is making an awe full lot of money on these devices, Apple invested billions and billions of dollars in R&D, design, production, marketing, distribution, stores, packaging,...
So in the end Apple is still taking a lot of profit on these devices, but not as much as you might think. In my opinion, they get paid for their hard work.
To answer your question why the iPhone costs more then the iPod touch, I think it's because, as you've pointed out, the design is quite similar so most of the costs of the iPod touch mentioned above (R&D, design,...) are already recouped with the iPhone, since the iPhone was released before the iPod touch.
Best Answer
Problem is solved after updating to iOS 11.