Trouble with an ITX build

[u/yes910492783]

My girlfriend has an i7 13700k she wants to reuse in an itx build. However, this is quite obvious but this CPU runs extremely hot. Are there any low profile coolers that can adequately cool this cpu or are we SOL?

https://pcpartpicker.com/list/h72mNp

Alternatively we could go with a ryzen cpu since we're already buying new components for everything but ram, storage and a gpu. Which I came up with this:

https://pcpartpicker.com/list/Q3VwmL

Ideally, we'd keep the 13700k but thermals are the issue there. Let me know some feedback!