Using iPhone as modem - battery damage I am using my iPhone as a modem, transfrerring a lot of data(4G) over long periods of time (awesome provider plan with lots of internet), connecting it to my laptop with the usb cable. I searched the web but i could not find a straight answer to the following question:

Am I damaginging the batter in any way by doing this? 
If I am, would it be less damaging to use WiFi?

I need do do this for a while, but I'm not sure if I can keep this up or if it would be better to get a separate device for internet connection (currently I'm putting my phone's SIM card into an old phone to be able to take calls and putting the internet's SIM card into iPhone)

I'll be grateful for answers and links that explain the matter if you have any.
So - looking over http://www.apple.com/batteries/maximizing-performance/ you should see that charging warms the device and your measured temperatures risk the device shutting itself off and permanent damage to the battery.

Yes, the battery is replaceable, but there's risk and cost there. I would tether over bluetooth or WiFi and disconnect the USB so that the unit doesn't have added heat load from the charging circuitry and chemistry (lithium batteries give off heat when charging) to keep the operating temperature of the iPhone to a level that's within Apple's recommendations.

Removing case or other external cooling might help a bit - but you can weigh the cost of an eventual battery replacement with the cost of a different tethering option and make your best choice.