When the ground is heated, the air will rise and keep rising. When the atmosphere is at high pressure, the rising air bubble is always cooler than the surrounding air. On the graph, the green line is always below the blue line. Under conditions of high pressure, the heated air will not continue to rise. Being cooler than the surrounding air, it will not rise.
High pressure leads to stable air conditions.
When the ground is heated, the air will not rise. If air does not rise, rain cannot condense. Convection rain requires a warm ground and low pressure. It causes short showers interspaced with sunny periods. The rain is caused by rapidly forming Cumulus and Cumulonimbus clouds.