No. Turtles don’t sweat as they do not possess sweat glands.
According to Apecsec.org, turtles appear to shed tears and it seems that it's their way to sweat.
In spending a life out at sea, there is a lot of salt exposure for the turtle. The glands in their eyes help remove the salt that they don’t need to survive, much like sweat through human skin.
To avoid poisoning themselves with salt buildup, sea turtles need to run these glands continuously to maintain the correct balance of salt in their bodies.
Turtles are fascinating to watch, and many have attractive colors and markings, and interesting personalities. They can make great interactive pets. However, a lot of work is involved in keeping a turtle.
Check out some tips all new turtle keepers need to know at Reptilesmagazine.com.