  A cosmological first-order phase transition is expected to produce a
stochastic gravitational wave background. If the phase transition temperature
is on the MeV scale, the power spectrum of the induced stochastic gravitational
waves peaks around nanohertz frequencies, and can thus be probed with
high-precision pulsar timing observations. We search for such a stochastic
gravitational wave background with the latest data set of the Parkes Pulsar
Timing Array. We find no evidence for a Hellings-Downs spatial correlation as
expected for a stochastic gravitational wave background. Therefore, we present
constraints on first-order phase transition model parameters. Our analysis
shows that pulsar timing is particularly sensitive to the low-temperature ($T
\sim 1 - 100$ MeV) phase transition with a duration $(\beta/H_*)^{-1}\sim
10^{-2}-10^{-1}$ and therefore can be used to constrain the dark and QCD phase
transitions.
