Caveat: It is not necessary to put the implementation in the header file, see the alternative solution at the end of this answer.

Anyway, the reason your code is failing is that, when instantiating a template, the compiler creates a new class with the given template argument. For example:

template<typename T>
struct Foo
{
    T bar;
    void doSomething(T param) {/* do stuff using T */}
};

// somewhere in a .cpp
Foo<int> f; 

When reading this line, the compiler will create a new class (let's call it FooInt), which is equivalent to the following:

struct FooInt
{
    int bar;
    void doSomething(int param) {/* do stuff using int */}
}

Consequently, the compiler needs to have access to the implementation of the methods, to instantiate them with the template argument (in this case int). If these implementations were not in the header, they wouldn't be accessible, and therefore the compiler wouldn't be able to instantiate the template.

A common solution to this is to write the template declaration in a header file, then implement the class in an implementation file (for example .tpp), and include this implementation file at the end of the header.

Foo.h

template <typename T>
struct Foo
{
    void doSomething(T param);
};

#include "Foo.tpp"

Foo.tpp

template <typename T>
void Foo<T>::doSomething(T param)
{
    //implementation
}

This way, implementation is still separated from declaration, but is accessible to the compiler.

Alternative solution

Another solution is to keep the implementation separated, and explicitly instantiate all the template instances you'll need:

Foo.h

// no implementation
template <typename T> struct Foo { ... };

Foo.cpp

// implementation of Foo's methods

// explicit instantiations
template class Foo<int>;
template class Foo<float>;
// You will only be able to use Foo with int or float

If my explanation isn't clear enough, you can have a look at the C++ Super-FAQ on this subject.

Just about every modern operating system will recover all the allocated memory space after a program exits. The only exception I can think of might be something like Palm OS where the program's static storage and runtime memory are pretty much the same thing, so not freeing might cause the program to take up more storage. (I'm only speculating here.)

So generally, there's no harm in it, except the runtime cost of having more storage than you need. Certainly in the example you give, you want to keep the memory for a variable that might be used until it's cleared.

However, it's considered good style to free memory as soon as you don't need it any more, and to free anything you still have around on program exit. It's more of an exercise in knowing what memory you're using, and thinking about whether you still need it. If you don't keep track, you might have memory leaks.

On the other hand, the similar admonition to close your files on exit has a much more concrete result - if you don't, the data you wrote to them might not get flushed, or if they're a temp file, they might not get deleted when you're done. Also, database handles should have their transactions committed and then closed when you're done with them. Similarly, if you're using an object oriented language like C++ or Objective C, not freeing an object when you're done with it will mean the destructor will never get called, and any resources the class is responsible might not get cleaned up.