For instance, in popular culture, such as Jinyong's Legend of the Condor Heroes, Genghis Khan is a secondary character, depicted as a smart leader who was shaped by the treachery of his own sworn brother and by the oppression of the Jurchen Jin dynasty. The reader is lead to empathize with Genghis Khan, through the eyes of Guojing, the patriotic Sung protagonist, despite the resentment that exists between him and Genghis Khan, the Mongolian leader who has decided to turn on their Sung dynasty allies.
I know Jinyong's work is fiction with a historical background, but I believe his work is a good indication of Chinese sentiments towards historical events and figures.
Chinese suffered as much as other conquered lands, to say to least. The Yuan dynasty lasted less than a century, one of the shortest period in the history. https://en.wikipedia.org/wiki/Genghis_Khan#Mixed
Even in the fiction `Jingyong`'s book, I wouldn't say the author had a bias favor Khan, I guess smart readers could read it from the book. The Khan would massacre every one if the be-seiged refuse to surrender, and they usually would drive herds of surrendered to the gate. Not to mention in the book the Kan is Kublai instead, and he is noway the secondary character.
That's in the sequel, The Return of the Condor Heroes, which depicts events after the death of Genghis Khan.
And since you mention Kublai, Genghis Khan only started the conquest of China. He only managed to conquer West Xia before his death. The rest of the conquest of China was done by his descendants, and so I believe most of the atrocities towards the Chinese occurred then.
https://www.reddit.com/r/AskHistorians/comments/27mism/how_i...
That said, there are still people pissed about the Mongol conquest. Genghis Khan is still hated in China, and central Asia and especially the middle east.