There are disclosed methods and apparatus for attachment and welding of tissue. In an embodiment, the apparatus includes an energy applicator configured to apply energy to generate heat within a target tissue to evaporate water to create dried tissue, and a thermally conductive material disposed adjacent the first tissue contacting surface or the second tissue contacting surface. The thermally conductive material may be configured for direct contact with the target tissue heated by the energy applicator. The thermally conductive material provides a high coefficient of thermal conductivity so as to evenly distribute heat within the targeted tissue area. Other embodiments are also disclosed.
