How to get rid of clothing moths?

These little buggers have been living rent free in my wardrobe for a while now. I have finally decided to stop being lazy and get rid of them. Problem is - I dont know how. I don't have enough space in the freezer to freeze everything. My only option is washing.

Would washing clothes on 60°C be enough to kill the eggs? The only clothes I will wash are the cotton/cotton blends. The few woolen jumpers I have have been put into the freezer at -19°C.

Is there any other thing I should do to ease the process of getting rid of these annoying pests?