  Transiting giant planets provide a natural opportunity to examine stellar
obliquities, which offer clues about the origin and dynamical histories of
close-in planets. Hot Jupiters orbiting Sun-like stars show a tendency for
obliquity alignment, which suggests that obliquities are rarely excited or that
tidal realignment is common. However, the stellar obliquity distribution is
less clear for giant planets at wider separations where realignment mechanisms
are not expected to operate. In this work, we uniformly derive line-of-sight
inclinations for 47 cool stars ($T_\mathrm{eff}$ $<$ 6200 K) harboring
transiting hot and warm giant planets by combining rotation periods, stellar
radii, and $v \sin i$ measurements. Among the systems that show signs of
spin-orbit misalignment in our sample, three are identified as being misaligned
here for the first time. Of particular interest are Kepler-1654, one of the
longest-period (1047 d; 2.0 AU) giant planets in a misaligned system, and
Kepler-30, a multi-planet misaligned system. By comparing the reconstructed
underlying inclination distributions, we find that the inferred minimum
misalignment distributions of hot Jupiters spanning $a/R_{*}$ = 3-20 ($\approx$
0.01-0.1 AU) and warm Jupiters spanning $a/R_{*}$ = 20-400 ($\approx$ 0.1-1.9
AU) are in good agreement. With 90$\%$ confidence, at least 24$^{+9}_{-7}\%$ of
warm Jupiters and 14$^{+7}_{-5}\%$ of hot Jupiters around cool stars are
misaligned by at least 10$^\circ$. Most stars harboring warm Jupiters are
therefore consistent with spin-orbit alignment. The similarity of hot and warm
Jupiter misalignment rates suggests that either the occasional misalignments
are primordial and originate in misaligned disks, or the same underlying
processes that create misaligned hot Jupiters also lead to misaligned warm
Jupiters.
