Do you know what to do if your cat has kittens premature?

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My moma cat had 2 little baby kittens not long ago. They seemed smaller then normal but they appeared healthy. It seemed like they were nursing ok. But in only a few days she moved 1 of them to my bed so I thought I'd pick the other one up for her. It had been laying in a certain postion for an hour or so but I thought it was just sleeping. I picked the tiny kitten up and was shocked to see that it was not alive. Then I noticed the other kitten was not doing good. I tried unsuccessfully to get it to nurse but it was to weak. Then I tried to get some milk from the mom but I wasn't able to do that; I wanted to save the kitten. The poor kitten died shortly thereafter. My son and I cried; we are still sad. I called the tiny kittens "bities" as in "little bities" or "wee wittle bities". Sadly we called numbers to find out how to discard the bities. And my son was told by animal control, or some office, to put them in 2 garbage bags and leave them out on the curb of the road. This happening was so sad. We are still sad over the kittens dieing. My son read online to late that premature kittens need to be kept very warm (95%). And our property manager did not fix our air conditioner correctly and I think it got to cold. We don't like it cold but we have to keep turning the thermastat on and off all the time. I wish I'd known certain things about premature kittens. I didn't realize they were premature; I just thought they were a little small. I didn't get a pic of them but here's a photo of moma Calli for you.