In the mini Kaiju 8 version you mentioned that Kafka looks for Bakko to curl up in the sun, in the giant n8 version the one looking for him is Bakko? I imagine it is a comical sight to see a tiger lying on the big Kaiju's head while he enjoys the sun or to take advantage when Kafka turns into the lizard version of a ball, the big cat seeks to stay more in the center to take advantage of the heat. The first time it happens, everyone panics because Bakko entered the quarantine zone an hour ago and hasn't left (it was at a time when they still didn't fully trust him), everyone sets up an operation expecting the worst. Or surprise, all they find is a little ball from which Kafka's half-asleep head emerges, trying to understand why they came in with weapons. The movement causes the big tiger to complain like a kitten because of the cold. Kafka, worried, thinking that he was hurt, He moves enough for everyone to see that the other is half asleep but saved. When Mina forces him out so she can leave, Bakko, even though he obeys, complains the whole way and turns his back on everyone angrily, this lasts while they don't let him back in.
Trust me when I say Bakko isn't the only one who take advantage of Kafka's surprisingly cool body. Birds, lizards and other small animals will perch on his massive body as its a nice comfy spot for sunbathing. Hell even an officer once got reprimanded for sleeping next to No.8.