This paper presents a novel methodology for the analysis of transient nuclear criticality in aqueous solutions of plutonium nitrate. The transient methodology includes one-dimensional thermal hydraulics and a detailed description of radiolytic gas formation (including aqueous concentrations of radiolysis species and bubble population, nucleation radius and advection velocity). The positive temperature feedback effect in dilute plutonium solutions, due to a low lying resonance (at 0.3 eV) in the microscopic fission cross section, is investigated. The solutions’ nuclear properties, such as intrinsic neutron source and mean neutron generation time; thermophysical properties and heat transfer coefficients; linear energy transfer and dynamics of radiolytic gas nucleation; and subcritical power, are also investigated. The effect of step and ramp reactivity insertions on transient nuclear criticality behaviour is examined, alongside the effect of fuel solution ingress and egress from the system. For a solution containing 16.0 g L−1 plutonium with an acidity of 0.2 mol L−1, increasing the width of the prescribed step reactivity insertion from 2.25 to 2.50 s increased the magnitude of the initial power peak, and decreased the time to boil, by an order of magnitude. It was observed that the characteristics of the radiolytic gas were dependent on the magnitude of the initial power peak. For example, the transients with the highest initial power peak produced an initially large quantity of radiolytic gas, with defined oscillations in their quantity (and other properties) as the transient progressed. For transients with lower power peaks, the oscillations became less defined, with a reduced period and magnitude, due to the lower quantity of radiolytic gas produced due to the initial power peak. Many of the presented simulations of nuclear criticality transients were terminated when the solution started to boil, a phenomenon which is not included in the presented methodology. Boiling occurred when the initial reactivity input induced a power spike that raised the solution temperature enough for the positive reactivity feedback effect to sustain the transient even when the reactivity input was removed.