The Cosori basket air fryers don't give off much heat from the bottom. Some folks like to use a wood cutting board or silicone mat underneath though to protect their countertops. I've got old corian at one place and haven't needed anything underneath the air fryer. Other place has new granite, so I do have a thin mat underneath the air fryer - just in case. I have this one: https://smile.amazon.com/gp/product/B0000E2GO6/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

The thing you do want to make sure you do is give space behind the air fryer. At least 5-6" clearance cause the vent/exhaust is out the back. It does warm up behind the air fryer.

As for when you take the basket out of the air fryer, definitely put it on something cause it's going to be hot.