Incremental emplacement of large silicic intrusions limits the size and lifetime of any magma chamber if earlier injected magma pulses solidify before the next pulse is emplaced. Geochronology indicates that long-term average magma fluxes of plutons are too low for the accumulation of magma volumes larger than a single pulse. To better constrain the formation of large-volume magma chambers, we investigate the influence of a changing emplacement rate of successive sill injections that form a composite intrusion in the upper crust. A thermal model with an explicit finite difference scheme simulates periods of transient high magma fluxes keeping the long-term average flux small. Several scenarios regarding how fluxes vary were analyzed. A progressive increase in flux does not result in magma accumulation. Only a step-like flux increase of at least one order of magnitude above the background flux produces a large magma reservoir. To generate a magma chamber of a melt-crystal mix above solidus temperature with a volume of 500–2000 km3, transient high fluxes of at least 1.25 × 10 − 2km3/a, equivalent to vertical, one-dimensional accretion rates of a few cm/a, are required. The transient high flux range where magma accumulates is largest for model scenarios with one period of transient high flux, and therefore, this emplacement style is favored for the built-up of substantial magma chambers during pluton growth. Intrusion scenarios with three and four periods of transient high fluxes do not generate reservoirs of mobile magma, but magma mushes can be present for some hundred thousand years.