If there is something inside the pc that is getting hot and starting to melt/burn, things may get worse.
Has the computer ever been opened up for cleaning and maintenance? Likely not as I understand your post.
"Smells" : burning smell, plastic smell, hot metal smell. Be more descriptive if possible.
Yes, you will need to open the case and inspect. Shutdown and unplug the power before doing anything.
Find a knowledgeable family member or friend to help you check the pc.
And update your post to include pc's full hardware specs and OS.
Knowing what we are working with is important.