Most warm Jupiters ( gas-giant planets with 0.1 ~ { } { AU } \lesssim a \lesssim 1 AU ) have pericenter distances that are too large for significant orbital migration by tidal friction .
We study the possibility that the warm Jupiters are undergoing secular eccentricity oscillations excited by an outer companion ( a planet or star ) in an eccentric and/or mutually inclined orbit .
In this model the warm Jupiters migrate periodically , in the high-eccentricity phase of the oscillation , but are typically observed at lower eccentricities .
We show that in this model the steady-state eccentricity distribution of the warm Jupiters is approximately flat , which is consistent with the observed distribution if we restrict the sample to warm Jupiters with detected outer planetary companions .
The eccentricity distribution of warm Jupiters without companions exhibits a peak at e \lesssim 0.2 that must be explained by a different formation mechanism .
Based on a population-synthesis study we find that high-eccentricity migration excited by an outer planetary companion ( i ) can account for \sim 20 \% of the warm Jupiters and most of the warm Jupiters with e \gtrsim 0.4 ; ( ii ) can produce most of the observed population of hot Jupiters , with a semimajor axis distribution that matches the observations , but fails to account adequately for \sim 60 \% of hot Jupiters with projected obliquities \lesssim 20 ^ { \circ } .
Thus \sim 20 \% of the warm Jupiters and \sim 60 \% of the hot Jupiters can be produced by high-eccentricity migration .
We also provide predictions for the expected mutual inclinations and spin-orbit angles of the planetary systems with hot and warm Jupiters produced by high-eccentricity migration .