what is the term that is used for doing surgery under low temperature? and what is the term used for doing transplantation of organs between twins?
There is not really an exact term for this, but there are several that address the issue of cold temperatures for medical therapy. Therapeutic hypothermia is probably the closest term to the definition you are looking for; it involves lowering the patient's body temperature with the goal of slowing both metabolism and disease process. It is done with some stroke and heart attack victims, and also during certain surgeries, such as heart transplants.
Cryosurgery is a related term which is generally used to refer to applying extreme cold to destroy tissues, such as removing a wart or a group of precancerous cells. Cryotherapy can involve chilling a single area of the body, such as the application of an ice pack, or can be used to chill the entire body briefly.