Given that both China & Pakistan have been against India in builtup history to 1971; and as Pakistan Radio just reported Chinese president: Pak-China friendship is higher than Himalayas, deeper than oceans and sweeter than honey
China wanted to avoid the war in South Asia as much as they could. They wanted Pakistan to come up with a political solution and to end it as soon as possible. Furthermore the Chinese realized that a war with India would not be as easy as it was in 1962.
India had a 'friendship treaty' with the Soviet Union, meaning that "Moscow and New Delhi [were] obliged to consult when either [was] threatened with attack. Since the Russians [were] known to want no part of a conflict that could bring China in on Pakistan's side, they [had] thus suggested that India move with care."
India was advised by the Russians to try its best to not provoke the Chinese into joining the war. And of course this treaty meant that the Russians were now involved in the war (In a limited support and advisory role, but still involved) so the Chinese were also being cautious not to escalate.
One of the reasons why the Chinese were so successful during their war with India was because the Indian army was caught by surprise. This was no longer the case in 1971, as India had fortified the border with China and were preparing for a possible Chinese retaliation. On top of this the Himalayan region was facing heavy snowfall, which would have made a Chinese advance into India much more difficult.
And finally, India's official involvement in the war only lasted 13 days. The Eastern Pakistan forces surrendered less than 2 weeks after Pakistan attacked India. A relatively short time for a war. The Indian army did not continue with its advance into West Pakistan. However, if it did and chose to continue the war, I doubt the Chinese wouldn't have stepped in.
Source: Time. 12/6/1971, Vol. 98 Issue 23, p34. 7p. http://content.time.com/time/magazine/article/0,9171,910155-1,00.html
India had built up its forces on the Indo-Chinese border after the 1962 war. This being the height of the Sino-Soviet split also aggravated the concerns there. Following the Border Conflict in 1969, the Soviets had built up their troops along the Chinese border and there would certainly be concerns of a flare up again in the case of overt Chinese action to support the Pakistanis.
China was successful in 1962 war because it backstabbed India. In 1971, India was fully prepared for China. The indian PM also warned China a full retaliation if it interfered. China had to stay put.