I would have come up with this solution,
=IF(A3="","",TEXT(A3,"ddd"))&IF(AND(A3<>"",C3="cool"),CONCATENATE("/",TEXT(A3+1,"ddd")),"")
But thanks to @John Jairo V I have learned something new today, I wasn't able to figure out this part of his formula "\/ddd" but then I google it and got to know...