I'm aware of the idea that the China entered the war in response to US aggression (i.e. crossing the 38th parallel, pushing north to the Yalu River), but were there any other motivations for intervening in korea. What did they hope to get out of the war?
They wanted to stick it to the US.
China in June 1950 was only about 7 months old. Prior to the PRC, the ROC was the government of mainland China and the US had been supporting them with money, weapons, and advice. Mao and the Communists wanted to kick the US off of mainland Asia and preferably out of Japan and Asia.
You need to look at it from a Sinocentric point of view. China's name translates as "Middle Kingdom", or more accurately, they are the center of the world. Chinese history stretches back millenia while the USA in 1950 wasn't even 200 years old, a blink of an eye when studying Chinese history. For generations, China and Japan had been vying for control of northeast Asia with Korea being stuck in the middle. Now, the Japanese were defeated and China was in a position to reassert itself in Northeast Asia except for the United States being there, too. From China's point of view, the US had backed her enemies (ROC) and was rebuilding another enemy (Japan) and was meddling in the affairs of their satellite/buffer state (Korea). By intervening in the war, they hoped to 1) kick the US out and 2) establish the old buffer state between China and Japan.