I have never heard of "upgrading" a train ticket in the way you would upgrade an airline ticket, i.e. pay the fare difference at the time of changing from 2nd to 1st class. If you decide to travel 1st class when holding a 2nd class ticket, there are usually 3 ways:
1. Given that you have a standard, flexible 2nd class ticket, cancel and return it, get the refund, buy a new 1st class ticket. May not work with a saver ticket or corporate ticket.
2. Use a voucher, that is sometimes given away if you are enrolled to DB's loyalty scheme, sometimes sold on ebay or redeemed with your points
3. Take a seat in 1st class and wait what will happen. If you're lucky, they are too lazy to calculate the fare difference and let you sit there, but most likely will charge the fare difference between standard tickets.

Anyway, personally I find 1st class on ICE trains anything else than overwhelming, with no real benefit than some dry nuts and a bit more space. If you don't travel on a Friday afternoon or Sunday evening you are quite likely to have 2 seats for yourself in 2nd class, this is enough space to work, relax or whatever. So I wouldn't bother about upgrading.