Would it be good secure programming practice to overwrite a "sensitive" variable before deleting it?

Is it good secure programming practice to overwrite sensitive data stored in a variable before it is deleted (or goes out of scope)? My thought is that it would prevent a hacker from being able to read any latent data in RAM due to data-remanence. Would there be any added security in overwriting it several times? Here is a small example of what I am talking about, in C++ (with comments included).

void doSecret()
{
  // The secret you want to protect (probably best not to have it hardcoded like this)
  int mySecret = 12345;

  // Do whatever you do with the number
  ...

  // **Clear out the memory of mySecret by writing over it**
  mySecret = 111111;
  mySecret = 0;
  // Maybe repeat a few times in a loop
}

One thought is, if this does actually add security, it would be nice if the compiler automatically added the instructions to do this (perhaps by default, or perhaps by telling the compiler to do it when deleting variables).