Kiwano Temple is a pretty spiky place so your first instinct is probably to try to scour the area, but the exact spike you need is elsewhere.
Luckily the spike isn’t too far away, nor is it too hard to get. Remember that huge spike on the professor’s desk at Chateau Chanterelle? That’s the key you need to get into Kiwano Temple, and the professor will be happy enough to give it to you.. once he’s not depressed anymore.
The professor is still face-down wallowing in his own emotions since Princess, his now-giant Chain Chomp companion, has run away. You’ve got to figure out how to get him out of his funk and it seems bringing back his beloved Princess is the only way to do so.
The professor’s assistant Toad mentions that Princess might come back if she smells her favorite snack, and if her rampage in the excavation site at Marmalade Valley is any indicator her favorite snack is bones.
You should still have the Bone card in your inventory. If not head back to Port Prisma’s Harbor District and squeeze a fresh bone for your card collection. Now head to Chateau Chanterelle.
Go into the backyard and press the Y button to use Cutout on these two boards next to Princess’s house.
Place the Bone card in the Cutout slot and wait for Princess’s return. After it’s all said and done the professor will give you the Sharp Spike on his desk.
All you have to do now is head back to Kiwano Temple, brave the spikes, and unlock the door to continue your quest to collect the Paint Stars and return color to Prism Island.