The tendency is to put wet shoes on or near a heat source to dry them. Unfortunately, this can shrink your shoes. You want to dry shoes at room temperature. Fill the shoes with newspaper or cloth to absorb the moisture in the inside.
This page contains the following solutions.
To dry tennis shoes after washing or to dry out any wet shoes, put them in front of the refrigerator vent grill. Open the laces wide, pull open the tongue of the shoe so the air can get inside and lay shoes on their side with the opening facing the grill.
To dry your shoes bunch newspaper together and stuff in the shoes. They will dry faster.
Now that it is boot season, many people in our family have wet insides of the boots after being outside. To make them dry faster overnight, stuff them with crumpled newspaper.