Coastal trapped Kelvin waves are important processes contributing to variability in the sea surface height and temperature near the coast. Field studies have measured large temperature fluctuations mainly made up of low-frequency internal Kelvin waves mostly of semi-diurnal tidal period at the continental shelf on the great barrier reef (Wolanski, 1983). Because they are balanced by Coriolis, in the Northern Hemisphere they remain fairly stable if they are propagating towards the North if the coast is on the right, or to the South if the coast is to the left.
My question is this: are Kelvin waves important in determining the surface temperature variations of regions that are, for example, on the west side of mountain slopes like the Andes or Rockies?
It is pretty clear that Kelvin waves and associated upwelling play a crucial role in introducing nutrients, larvae and other components into the ocean's coastal regions (relatively cold water). However, the connection between surface temperature variation in the coastal waters and the temperature in the regions west of mountain ranges you mention is not so clear.
One thing that could happen is that, because upwelling is associated with relatively cool water being introduced to the near shore from the deep abyss, the coastal marine layer will have a lot of moisture. As the moisture laden air traverses a coastal mountain range, it will rise due to orographic lift and cool adiabatically, thereby raising relative humidity all the way to 100% resulting in rain. So the coastal side is cool and wet, whereas on the other side of the coastal range it will be much warmer and drier.
Wolanski, E., and G. L. Pickard. "Upwelling by internal tides and Kelvin waves at the continental shelf break on the Great Barrier Reef." Marine and Freshwater Research 34.1 (1983): 65-80.