Hi I am going to Datong next, Chinese New Year, and I wonder if it could be a problem that many people travel there, so they could not let so many go inside??

It is hard to tell. Generally speaking, the tourists are not so much as that during the National Holiday, so the problem may not exist as you mentioned.
Even though you meet many people, you can still wait to enter the temple. According to the rules, altogether about 80 people are not allowed enter at the same time. But if you wait, you can still enter there, so please do not worry.

Chinese New Year's golden week - a peak period in terms of tourist numbers!!!