Convective self-aggregation is a modelling paradigm for thunderstorm organisation over a constant-temperature tropical sea surface. This setup can give rise to cloud clusters over timescales of weeks. In reality, sea surface temperatures do oscillate diurnally, affecting the atmospheric state. Over land, surface temperatures vary more strongly, and rain rate is significantly influenced. Here, we carry out a substantial suite of cloud-resolving numerical experiments, and find that even weak surface temperature oscillations enable qualitatively different dynamics to emerge: the spatial distribution of rainfall is only homogeneous during the first day. Already on the second day, the rain field is firmly structured. In later days, the clustering becomes stronger and alternates from day-to-day. We show that these features are robust to changes in resolution, domain size, and surface temperature, but can be removed by a reduction of the amplitude of oscillation, suggesting a transition to a clustered state. Maximal clustering occurs at a scale of l max ≈ 180 km, a scale we relate to the emergence of mesoscale convective systems. At l max rainfall is strongly enhanced and far exceeds the rainfall expected at random. We explain the transition to clustering using simple conceptual modelling. Our results may help clarify how continental extremes build up and how cloud clustering over the tropical ocean could emerge much faster than through conventional self-aggregation alone. Currently, general circulation models cannot simulate organised deep convection as these models describe convection as a collection of non-interacting convective cells. Yet, the increase in tropical rainfall was stated to predominantly stem from organised deep convection. 1 Similarly, in midlatitudes, the majority of flood-producing rainfall was attributed to mesoscale convective systems (MCSs), 2,3 that is, long-lived complexes of thunderstorms spanning ∼ 100 km in diameter. 4 In self-aggregation studies pronounced clustering occurs on the timescale of several weeks. 5-7 There, the radiative convective equilibrium scheme (RCE) 8,9 is usually employed, assuming spatially and temporally constant surface temperature (∼ 300 K). In self-aggregation, radiation feedbacks have emerged as the "smoking gun" for sustaining and increasing clustering. 5 Still, factors such as sea surface feedbacks, 10 domain size, geometry, and resolution, 11 as well as cold pool effects, 12,13 all contribute.Prescribing constant boundary conditions is an elegant model simplification, but not always realistic. Especially under weak surface wind conditions and strong insolation, sea surface temperature amplitudes were observed to be as large as two 14,15 to five kelvin 16 and suggested to modify atmospheric properties. 16 Such temperature variations may even affect the Madden-Julian Oscillation arXiv:2001.04740v1 [physics.ao-ph]