Is the Earth heated up by the tides?
A good estimate of the lunar tidal energy dissipated into the oceans is 2.5 Terawatts (Munk, 1997; Le Provost &amp; Lyard, 1997). The value estimated comes mainly from two different sources: from harmonic calculations and from altimetry estimates using satellite observations (e.g., Topex/Poseidon).

The input of energy into the coastal ocean is not uniform and has a peak in the South Atlantic Ocean, while the energy is dissipated by bottom friction in the coastal ocean and mainly in the North Atlantic Ocean (Le Provost &amp; Lyard, 1997).
 

Source: Nature: Egbert &amp; Ray, 2000. Estimates of tidal energy dissipation.

Egbert &amp; Ray (2000) showed that a fraction of the dissipation (1 TW) takes place in the deep ocean in areas of, generally near areas of rough topography. Maintaining ocean stratification and the large scale thermohaline circulation (the commonly known "Conveyor Belt") requires around 2 TW to provide enough mixing (Munk &amp; Wunsch, 1998). Therefore, the tides provide about half of that energy with the other half coming from wind forcing.

Here is a summary figure from Munk &amp; Wunsch, 1998. 

The repercussion of this fact are given by Wunsch (2000):


  ...it was only recently recognized that the need for an energy source to sustain the vertical mixing (lifting dense water through lighter) has important consequences. The difficulties of driving fluid motions by surface heating and evaporation mean that a mechanical source of energy must control not only the directly wind-driven flows, but also the deep-water components of the meridional overturning circulation. 
  
  ... changes in tidal distributions and the consequent mixing would need to be understood over geological time. During the Last Glacial Maximum, the sea level was about 130 metres lower than today. This configuration removed much of the present regions of shallow-water energy dissipation and changed the deep-ocean tides, presumably affecting oceanic heat transport. Over longer periods in the past, the entire continental configuration was different, with radically different tidal distributions and mixing. It appears that the tides are, surprisingly, an intricate part of the story of climate change, as is the history of the lunar orbit.