Heat is a term used in more than one facet of the U.S. dairy industry. In one interpretation, dairy cows or heifers are inseminated with a selected service sire after heat (estrus) is detected. This is a crucial step for dairy cows to calve and begin lactating. An alternative interpretation is the excessive environmental heat that can negatively impact dairy cattle health and production. To make improvements in both heat topics, selection tools such as phenotypic or genomic evaluations can be established. The purpose of this dissertation was to investigate these two areas impacting the U.S. dairy industry, develop predictions, and refine the method used for genomic predictions. Phenotypic predictions were calculated for beef service sire fertility when mated to dairy cows and heifers to successfully produce more valuable crossbred calves. The phenotypic predictions of bull fertility are referred to as sire conception rate (SCR). Two genomic estimated breeding values (GEBV) were established for heat tolerance of production yields. The heat tolerance GEBV (GEBV_ht), is the slope of milk, fat, and protein yield under heat stress for one unit of temperature-humidity index (THI) above the heat threshold. The heat tolerance GEBV at a given heat load (GEBV_(ht_HL )) is the combination of GEBV_ht, genetic merit of production without heat stress, and the number of THI units above the heat threshold. Both GEBV_ht and GEBV_(ht_HL ) were genomic predictions calculated with single-step genomic best linear unbiased prediction (ssGBLUP). The theoretical properties of the genomic relationship matrix construction in ssGBLUP were also investigated to ensure predictions were not biased. It is theoretically more robust to scale the genomic relationship matrix (G) to the pedigree relationship matrix of genotyped animals (A_22) and then add a small portion of a positive definite matrix such as A_22 to G. Changing the order of operations does not have an impact on the genomic relationship matrix, GEBV, single nucleotide polymorphism (SNP) effects, or indirect predictions (IP) on the genomic base. However, adding A_22 to G prior to scaling G to A_22 will result in biased IP on the pedigree scale, depending on the utilized proportion of A_22.