Cdc7/Hsk1 is a conserved kinase required for initiation of DNA replication that potentially regulates timing and locations of replication origin firing. Here, we show that viability of fission yeast hsk1Δ cells can be restored by loss of mrc1, which is required for maintenance of replication fork integrity, by cds1Δ, or by a checkpoint-deficient mutant of mrc1. In these mutants, normally inactive origins are activated in the presence of hydroxyurea and binding of Cdc45 to MCM is stimulated. mrc1Δ bypasses hsk1Δ more efficiently because of its checkpoint-independent inhibitory functions. Unexpectedly, hsk1Δ is viable at 37°C. More DNA is synthesized, and some dormant origins fire in the presence of hydroxyurea at 37°C. Furthermore, hsk1Δ bypass strains grow poorly at 25°C compared with higher temperatures. Our results show that Hsk1 functions for DNA replication can be bypassed by different genetic backgrounds as well as under varied physiological conditions, providing additional evidence for plasticity of the replication program in eukaryotes.