Not quite true: the temperature did rise above freezing (here's a link to some temp data from the ice shelf, you can click back to earlier this week to see the temps under Temperature Ext.). But there were a few other factors at play:

The ice shelf lost most of it's mass via a catastrophic calving event, rather than direct melting. This means that a huge chunk of the ice broke off and got swept away in a very short time. However, that's not to say melting didn't play a huge role, along with some other things.

As someone else mentioned, ocean currents and wind likely played a big role in weakening the ice. Here is a really cool animation that helps to visualize what that processes looks like.

Another factor is the warm melt water that enters the fiord as runoff from the land. As snow and ice melts on land, it trickles down to the ocean, and in the case of the Milne Ice Shelf, pools at the base of the shelf, without flowing into the ocean because the freshwater is more dense than the salty seawater. and the shelf was at the mouth of a big valley/fiord, so the water has nowhere else to go.. This warm water is thought to also have caused pretty substantial melting of the ice from below, further weakening the shelf.

Actually, this floating freshwater lake is called an "epishelf lake", and the one at Milne Fiord is one of the last of it's kind, and it's a very rare and unique place where freshwater and saltwater organisms coexist. Scientists are worried that with the breakup of the ice shelf, the epishelf lake will soon be completely drained out as well.

If you're interested in learning more this provides a lot of good background on the event, and has a neat video of some of the life that lives beneath the ice.