Without seeing the pattern, it's hard to say just how many stitches you need to increase.
One way to easily increase the size of a pattern is to use thicker yarn and larger needles. That automatically increases the size.
If it's a simple pattern--one without a design in the knitting, then you can measure how many stitches per inch you got with the smaller hat. Once you know that figure, you can use it to determine how many stitches to cast on for a larger one.