On sci.space.tech, Jason C. Goodman once wrote:
  On Earth, the atmosphere and ocean carry about equal amounts of heat;
Frank Crary's got the right idea when he suggests fluid motions would
temper the climatic extremes.  A nonrotating world will have much more
efficient thermal recirculation; on Earth, the Coriolis force requires
winds and currents to move nearly perpendicular to thermal gradients,
rather than straight downgradient.
  I'm a graduate student in climatology; I sat down and thought about
this problem for a few hours, and cooked up a "box model" for a
nonrotating Earthlike planet, in which the day-side and night-side boxes
attempt to reach hot and cold equilibrium temperatures while thermal
pressure-driven winds carry heat from warm to cold.  I'm not sure I
believe the result: the atmosphere can carry heat to the cold side so
efficiently on a nonrotating planet that the temperature difference is
only 5-15 degrees C!  The winds in this model are 250 m/s!
  If this is true, expect tropical weather with constant torrential
rains in the "noontime", winds stronger than any Earthly tornado
constantly during "morning" and "evening", and calm, clear, cool nights.
  I'll check this result later; model details available on request.
 
There was some dispute, and Goodman agreed that box models may not be the best way to answer this kind of question. Later, when he tried to use a more sophisticated model to check his results, it "blew up" on him, so the question remains somewhat open.