Can my kitten get sick?

 
Can my kitten get sick?
I know this sounds really mean but my mother is over protective about toxoplasmas in cats. So she makes my kitten stay in the garage. It is very cold in there but very roomy and comfy with carpetting coahes and no bugs. its very clean and bed room like. Will he get scared alone? will he get sick? and is it too cold?its about 38 degress outside and about probably 60 degress inside the garage. it might get colder.
If you guys are making your cat live in your garage, you might as well not even have one. That's cruel.
nope i dont think soo ... hes lucky hes not livving outside so inside the grage is perfectt