I know in Iran, many have considered Mongols in a negative light. Yet 100s of years later, other rulers in Iran, including Timur and Nader Shah, still idolized Chengis Khan.
After the Mongol empire collapsed, did any rulers in China or Russia continue to idolize the Mongols? How was their legacy regarded amongst the Tsars of Muscovy and Imperial Russia? How did the Ming and Qing dynasties view the legacy of Chengis Khan?
Ok on Russia the answer is no. With a few honourable exceptions there are two, massively flawed, basic attitudes Russian historians down the ages have taken. Firstly they often deny that the Mongols had any major impact on Russian civilisation. They claim that the Mongols had little presence in Russia and furthermore their barbarity and lack of sophistication meant that there was nothing worth copying from them. Secondly they portray any Mongol influence as entirely negative portryaing their actions as being limited to looting, extracting tribute, raising cities and massacring scores of people. Furthermore a large part of the Russian historical narrative was based around their struggle to throw off the Mongol Yoke. The doing of which inspired a lot of nationalist mythologisation of the freeing of Russia. This tendency even persisted under the USSR. While they managed to get away from outright racism that characterised a lost of Tsarist study they kept the same assumptions that saw Mongol rule in entirely negative terms and added a Marxist twist. They basically classified the Mongol empire as having a feudal structure and from this went on about the inherent exploitation of this system. This may well have also been influenced by fears of Mongolain nationalism. Mongolia was in the Soviet sphere during the Cold War and served as a buffer with China. In attempt to suppress potential nationalist sentiment they even went so far as to destroy some historical artefacts such as Genghis Khan's spirit banner and a variety of old manuscripts on the subject. Interestingly Soviet scholars had an argument with Communist China over the historiography of the Mongol empire. The Chinese had a more positive view of the Mongols, which brings me on nicely to how China viewed the Mongols.
Ok early Chinese historiography of the Mongols is kind of complex. Early on the Ming dynasty, while not particularly keen on the Yuna dynasty, was prepared to offer some praise. They accepted the Mongol conquest as a signal that they had the mandate of heaven and thus the right to rule. They also express some admiration for the fact that the Yuan ruled an incredibly large empire. However, rather amusingly, they just see this as the extension of the Chinese empire. They couldn't really accept the fact that China was absorbed into something bigger than itself. They also provide some criticism for issues such as the Mongol reluctance to promote the Chinese to important posts, abolition of certain branches of government and Mongol favouring of Buddhism. However after the Tumu Crisis, when the Oirat Mongols captured a Chinese emperor, commentaries take on a more negative tone. The flaws of the Yuan dynasty are increasingly emphasised and the Yuan military expeditions become seen as serving no purpose other than plunder and glory hunting, unworthy of an emperor and a waste of lives. There's also a marginalisation of the Mongols in terms of their perceived significance in Chinese history, they're sometimes portrayed as a somewhat of a blip and outside normal Chinese history (and thus not really worthy of study). There were a few books that still praised the Yuan dynasty but these were in the minority. The Qing, perhaps because of their own steppe origins, take on a rather more positive view of the Mongols stopping the printing of some of the more nationalist condemnations of the Yuan dynasty. In other books that were still made we can occasionally find rather tart little notes condemning some of the more blatant criticism of the Mongols.
Now what of Communist China's attitude that I hinted at earlier and then tantalisingly whipped away from. During the 1960s we see some increasingly positive assessments of the Mongols. They emphasised elements such as the Mongols managing to reunify the northern and southern halves of China, the development of crafts and trade and also saw the Mongols as allowing other cultures to come into contact with, in their eyes, more advanced Chinese civilisation. Indeed during one historical spat with the Soviets they rather insultingly suggested that Russia should be grateful that the Mongols allowed them to be exposed to a more advanced culture.