I have this cutting of unknown variety in a container with 100% perlite for almost 7-9 months now.

About 3-4 months ago I noticed that it grew a tiny 0.5 inch root. Since then no growth was observed, so I got a heat mat and kept it on it for about 3 months. Weather is getting warmer in Australia and I see a few bumps on the side as well as minuscule new leaves starting to shoot out at the top, so I moved them outside under the full sun for 2 weeks. We've had several hot days 32c / 90f but average max is probably 26c/79f and min 19c/66f.

And today, to my dismay, I noticed that one of the tips is turning black and very soft to touch (rotten), and all the baby leaves starting to grow are burnt dead and gone. Perhaps the direct sun was too much, too soon. I should have waited till I saw a few new leaves. Also we had heavy rains recently. It's very windy and low humidity, so the perlite should dry up quickly in this condition.

Now I have moved it back inside and placed it on the heat mat. What should I do with the rotten tip? It's about 1 inch of that green part. The other tip is fine and the stem itself is still hard. Images attached.