The doctors I’ve been to have solved this problem by putting their hands in ice water just before the exam.
On a tangential note, I understand that sometimes men in a serious accident will get an erection for some reason. Emergency room nurses in this situation give it a good thwack to free up blood that could be more useful elsewhere in the body.
Good idea.
BTW, years ago…I had one young, female, examiner do more than, ahem, examine. Very cool experience. That really made my day!