The effect of modified equator-to-pole temperature gradients on the jet stream by low-level polar warming and upper-level tropical warming on jet streams is not fully understood. We perform four aquaplanet simulations to quantify the impact of different sea surface temperature distributions on jet stream strength, wave amplitudes and jet stream waviness, quantified by a modified Sinuosity Index. A large-scale uniform warming scenario increases the jet strength whereas decreases in jet strength occur in two scenarios where the meridional temperature gradient is reduced. However, all scenarios indicate substantial decreases in the magnitude of large wave amplitudes, jet stream extreme waviness and reduced variability of these diagnostics, suggesting a relationship with weakened baroclinicity. Our findings contradict the earlier proposed mechanism that low-level polar warming weakens the jet stream and increases wave amplitudes and jet stream waviness. We conclude that a weaker jet stream does not necessarily become wavier.