Large volcanic eruptions strongly influence the internal variability of the climate system. Reliable estimates of the volcanic eruption response as simulated by climate models are needed to reconstruct past climate variability. Yet, the ability of models to represent the response to both single-eruption events and a combination of eruptions remain uncertain. We use the Community Earth System Model version 2 along with the Whole Atmosphere Community Climate Model version 6, known as CESM2(WACCM6), to study the global-mean surface temperature (GMST) response to idealised single volcano eruptions at the equator, ranging in size from Mt.\ Pinatubo-type events to supereruptions. Additionally, we simulate the GMST response due to double-eruption events with eruption separations of a few years. For large idealised volcanic eruptions, we demonstrate that double-eruption events separated by four years combine linearly in terms of GMST response. In addition, the temporal development is similar across all single volcanic eruptions injecting at least \(\SI{400}{\tera\gram(SO_{2})}\) into the atmosphere. Since only a few eruptions in the past millennium occurred within four years of a previous eruption, we assume that the historical record can be represented as a superposition of single-eruption events. Hence, we employ a deconvolution algorithm to estimate a historical GMST response pulse function for volcanic eruptions, based on climate simulation data from 850 to 1850 taken from a previous study. By applying the estimated GMST response pulse function, we can reconstruct most of the underlying historical GMST signal. Furthermore, the GMST response is significantly perturbed for at least seven years following eruptions.