In a “hothouse” climate, warm temperatures lead to a high tropospheric water vapor concentration. Sufficiently high water vapor levels lead to the closing of the water vapor infrared window, which prevents radiative cooling of the lower troposphere. Because water vapor also weakly absorbs solar radiation, hothouse climates feature radiative heating of the lower troposphere. In recent work, this radiative heating was shown to trigger a shift into a novel “episodic deluge” precipitation regime, where rainfall occurs in short, intense outbursts separated by multi‐day dry spells. Here, we further examine the role of the lower tropospheric radiative heating (LTRH) in the transition into the “episodic deluge” regime. We demonstrate that under high sea‐surface temperature the “episodic deluge” regime could be formed even before the LTRH turns positive. In addition, we examine whether these oscillations operate on larger scales and how these oscillations, which represent “temporal” convective self‐organization, would manifest in the presence of traditional “spatial” self‐ or forced‐aggregation in large‐domain convection‐permitting simulations. We find that the temporal oscillations become much less synchronized throughout a large domain ( 1,000 km) because gravity waves cannot propagate fast enough to synchronize convection. We also show that temporal oscillations still dominate the rainfall distribution even when there is tropical convective self‐aggregation or a large‐scale overturning circulation. These results could have important implications for extreme precipitation events under a warming climate.