"进行得非常热烈" can be translated into English as "proceeded with great enthusiasm" or "was carried out very enthusiastically".
Here are some example sentences to illustrate the usage:
1、 The meeting proceeded with great enthusiasm, and everyone actively participated in the discussions.
（会议进行得非常热烈，每个人都积极参与了讨论。）
2、 The event was carried out very enthusiastically, with a lively atmosphere throughout.
（活动进行得非常热烈，现场气氛一直很活跃。）