Hello,
I apologize if this is a fairly basic question. I'm new to Houdini and struggling to find the proper search terms to find answers to my questions. I work primarily in C4D and I've been following this tutorial [www.youtube.com] on melting an object using Heat Within Object.

I have 2 main questions: how do I bake this sim so it doesn't need to calculate every time I run it? And how can I export it as a mesh into C4D?

I'll attach the HIP file even though it is pretty much identical to the tutorial. Thank you in advance for any help!

What you are looking for is File Cache https://www.sidefx.com/docs/houdini/nodes/sop/filecache.html [www.sidefx.com]

You can probably export the cache out to C4D with Alembic
https://www.sidefx.com/docs/houdini/nodes/out/alembic.html [www.sidefx.com]
You can export a Alembic directly from within your SOP with a “Alembic ROP output driver” SOP
Hope that helps