Despite the high abundance of Aquificae in many geothermal systems, these bacteria are difficult to culture and no viruses infecting members of this phylum have been isolated. Here, we describe the complete, circular dsDNA Uncultivated Virus Genome (UViG) of Thermocrinis Octopus Spring virus (TOSV), derived from metagenomic data, along with eight related UViGs representing three additional viral species. Despite low overall similarity among viruses from different hot springs, the genomes shared a high degree of synteny, and encoded numerous genes for nucleotide metabolism, including a PolA-type DNA polymerase polyprotein with likely accessory functions, a DNA Pol III sliding clamp, a thymidylate kinase, a DNA gyrase, a helicase, and a DNA methylase. Also present were conserved genes predicted to code for phage capsid, large and small subunits of terminase, portal protein, holin, and lytic transglycosylase, all consistent with a distant relatedness to cultivated Caudovirales. These viruses are predicted to infect Aquificae, as multiple CRISPR spacers matching the viral genomes were identified within the genomes and metagenomic contigs from these bacteria. Based on the predicted atypical bi-directional replication strategy, low sequence similarity to known viral genomes, and unique position in gene-sharing networks, we propose a new putative genus, “Pyrovirus,” in the order Caudovirales.