Depends on quality. If their old vintage they won't shrink. If they are new poor quality you can count on shrinking. High quality very very expensive probably not much. On the other side of the coin look at it this way who would want sheets that can't be washed in hot or at least very warm.

.Did you already buy ?

I use warm pp cycle. 10-15% shrinkage first wash, none afterwards.

I have two sets. I wash on hot. The ones I have bought (Linoto) come prewashed. They are par-dried in dryer and then airdried. No shrinkage.

But Chinese made or lower quality/lower thread count goods might shrink.

I affirm what rococogurl has stated. LINOTO comes prewashed and I have noticed little shrinkage. I researched genuine linen sheets before our purchase and concluded that LINOTO is the best... top quality linen from Europe and made in the USA. They cost more but I wager the sheets will last a long time. Our set is 3 years old and shows few signs of wear. The linen sheets are in rotation with a cotton set and see 2 weeks per month of use.

My mains are Parachute, pre-washed. No shrinkage. Sizes are still quite generous.

Linoto is 3rd, IMO. Rough Linen, USA, Parachute (Portugal made), Linoto.

There are some linen sheets from Canada but they are not budget friendly. Awesome? Yes.