How do I keep my kitten from peeing on my bed?

My boyfriend and I recently adopted a Siamese kitten from the pound. They told me that he was probably 12 weeks old when I got him fixed last week. He is very good at using the litter box, except when he pees. Before we got him fixed he peed everywhere. Now, he just pees on my bed at night. I was told that fixing him would stop this problem. Does it take some time? Should I just cage him at night for the rest of his life? If anyone else has had similar problems that they fixed I would love to hear tips.