Why are solar telescopes built on lakes? The telescope big bear is located in the Southern California.
According to the wikipedia page, water can cool the observatory.
Is it better to build it on a cold high mountain with stable and clear atmosphere?
What is the difference when building a solar and an optical telescope?  Optical telescopes are usually not build on lakes.
To amplify andy256's comment, the problem that solar telescopes face is that heating of the surrounding ground during the day gives rise to turbulence in the air near the ground, making the observing conditions worse (think of the heat shimmer just above the surface of hot pavement or a hot road -- that's turbulence bad enough for your naked eyes to notice). Since water has a high thermal inertia, it doesn't heat up as much as land does, so you get less turbulence. (Another approach is to put the telescope on top of a tower, above the worst of the turbulence.)

Note that Big Bear is at an altitude of 2,000 meters, so it is at a moderately high altitude.