Of course there are some ways to update the firmware through iTunes on a frozen iPhone, but we need to put this problem into two parts, one part is to fix the freezing issue on iPhone, and the other part is update iPhone with a selected version of iPhone firmware.
Part 1. How to fix a frozen iPhone
The first thing you need to do is to fix the frozen iPhone, and there are several methods you can try them one by one.
Method 1. Restart
Many problems of iPhone can be solved by restarting, and you can also try it for a frozen iPhone. Just press the Home and the Power button simultaneously until the Apple logo comes back on again.
Method 2. Reboot
If the method 1 couldn’t worked, you may need a third-party software to reboot your iPhone, here is an free iPhone reboot tool enables you to fix iPhone freeze problem, the software only has two buttons, “Enter Recovery Mode” and “Exit Recovery Mode”, with it, you can fix iPhone freeze with only one click.
Part 2. Update iPhone with a selected version of iPhone firmware.
Step 1. Hold the SHIFT key while clicking the "Update" or "Restore" button in the iPhone tab in iTunes.
Step 2. Then a dialog box will come up which will allow you to select the firmware file to use for your update. Just select the version of firmware you want to update.
Now you complete the upgrade of firmware on your frozen iPhone.