Most size recomendations are minimums, if the image is larger the site should down scale to the correct size but a smaller image will not be scaled up because it will distort the image.
The the minimum heigth isn't specified, it can be any height.
Banner / Header: 960px x 320px
Featured Image: 650px wide (to take up full width of post)
Marketing (Call to Action Image): Width 328px, Maximum Height of 300px
Featured Image: 820px wide
Banner: 1200px x 400px
Logo: 360px x 70px
Author Image: Author photo image. Recommended size is 512px x 512px.
Video: 800px wide
Book: 185px x 260px