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De novo mutations (DNMs) in the germline have long been identified as a key element in the causes of developmental and other genetic disorders. Previous attempts to investigate genetic factors affecting DNMs have suffered from a lack of statistical power, due to the difficulty of obtaining a sufficient number of parent-offspring trios. Thus, the rare disease cohort of the UK’s 100k Genomes Project (100kGP), comprising more than 10,000 trios, represents an unprecedented opportunity to investigate the genetics of germline mutation. Here we estimate SNP heritability of DNM count in offspring, as a measure of the relative contribution of genetic factors to the variance of the trait, in a PCA-selected subset of the 100kGP cohort. We estimate separate SNP heritabilities for paternally and maternally transmitted mutations (based on parentally phased DNMs in offspring), computed using parental genetic variants at a range of minimum frequencies and a variety of methodologies. We estimate a heritability of 10-20% for paternal DNMs; by contrast, for maternal DNMs we find no significant evidence for non-zero heritability. We investigated the partitioning of heritability among genes with different expression profiles in different tissue or cell states, and found a relative heritability enrichment for genes expressed in gonadal tissues, particularly testis. Among germ cells in adult testes we observed relative enrichment of heritability in genes associated with the (undifferentiated) spermatogonial stem cell state.