Yes, a 55% linen/45% cotton sweater will shrink in the dryer.
Cotton can be washed in warm temperatures, but may shrink in a dryer. The higher the heat and the longer the drying cycle, the more likely the fabric is to shrink. Machine-drying cotton can become tricky since it requires a relatively high heat to properly dry cotton, but too much heat and it will shrink.
Linen is even more susceptible to shrinking due to heat than cotton. The upside to linen is its durability and resistance to soiling. The tradeoff is that it is not as soft as many other fabrics. Washing and drying linen a few times will soften it up, however continued/regular washing and drying will cause fading and shrinkage.
Ideally a 55% linen/45% cotton garment should be purchased a little bigger than desired. It can then be machine-washed and machine-dried a few times to soften up the linen component of the blend and the accompanying shrinkage won’t be an issue since it was purchased with room to shrink. After that, dry-cleaning will prevent any further shrinking or fading.
A linen/cotton blend may wrinkle easily; luckily it is safe to iron.
You can still make a difference in how your clothes look by taking appropriate steps to reduce shrinking and stretching by using the right laundry techniques. Check out some tips on how to prevent clothes from shrinking and stretching shared by About.com.