No, not true. Well, yes, it’s that hot, but not all sherbet/sorbet is iced. Sometimes it is a drink. The original word derives from the Arabic term “to drink” (shariba) and in modern Turkiye, you can still find it as a drink.
Sherbet can be had in many flavors deriving from herbs, fruits, and other plants. Some specific flavors are famous in certain locations, such as Bursa’s peach flavor (Bursa is the old capital of Ottoman Empire) or ingredients such as musk.
I had the one in the photo at the Women’s Cooperative in Adana. We didn’t ask for it. It was offered with the coffee. I think of the sherbet drink as being similar to Ribena in Germany or fruit punch in the USA. It’s a version of electrolytes.
If you want to read more about this, check out this article from the Slow Food Movement.