How do i make an ice biome

Hey so I'm trying to make an ice cave biome and I don't know how to make it spawn near ice/snowy biomes. I tried setting the temperature to 0.0 and -0.5 but to no avail, maybe I could change the raining possibility or biome heights but I don't know what values can group it with other snow biomes. Oh, also how do I cover the entire cave biome with my custom cave block? Since if I put the Ground block and Underground blocks to my custom block it'll still generate stone on the ceiling, I don't want that.