What does Gu Beiqing mean by singing cold songs?

Search is one of the screen names of lovers, and the complete one is:

Guide tea is warm

Gu Beiqing sings cold songs.

So I guess there is a possibility:

1, your ex-boyfriend wants to use the couple's screen name with you;

2, jump off the couple's online name or something, he thinks this sentence is very suitable for him, and his heart is lonely;

3. Further, he wants to express his love euphemistically, and send you "Gubei QingHan Ge", expecting you to spend time with your mother and then have a look.

"Know the warmth of southern tea" and then express the meaning of "I think you are a warm and loving sister".

These are all my brain holes for reference only.