The soup is cold, I help you warm up the soup.

[mampwamp]

The soup is cold, I help you warm up the soup.
The soup is cold, I help you heat up the soup.

Which word is more commonly used?

 

[Tdol]

You can use both. I guess that heat up is more common, but others may feel differently. I would use I'll help you.

 

[Rover_KE]

Where did you encounter these sentences, mampwamp?

In both cases the comma should be a semicolon.

 

[emsr2d2]

It would make more sense if it said "I will help you heat up/warm up the soup" after a semi-colon or a full stop.

 

[Tdol]

In both cases the comma should be a semicolon.

I missed that.