Multidrug-resistant Gram-positive bacteria, including bacteria from the genus Staphylococcus, are currently a challenge for medicine. Therefore, the development of new antimicrobials is required. Promising candidates for new antistaphylococcal drugs are phage endolysins, including endolysins from thermophilic phages against other Gram-positive bacteria. In this study, the recombinant endolysin LysAP45 from the thermophilic Aeribacillus phage AP45 was obtained and characterized. The recombinant endolysin LysAP45 was produced in Escherichia coli M15 cells. It was shown that LysAP45 is able to hydrolyze staphylococcal peptidoglycans from five species and eleven strains. Thermostability tests showed that LysAP45 retained its hydrolytic activity after incubation at 80 °C for at least 30 min. The enzymatically active domain of the recombinant endolysin LysAP45 completely disrupted biofilms formed by multidrug-resistant S. aureus, S. haemolyticus, and S. epidermidis. The results suggested that LysAP45 is a novel thermostable antimicrobial agent capable of destroying biofilms formed by various species of multidrug-resistant Staphylococcus. An unusual putative cell-binding domain was found at the C-terminus of LysAP45. No domains with similar sequences were found among the described endolysins.