Are local variables always volatile?

Question

Are local variables always volatile in C#?

In other words, is the volatility of num the same in these two classes:

public sealed class ThreadSafeObjectA
{
    private volatile int num;
    public int DoThing() => num = 1;
}

public sealed class ThreadSafeObjectB
{
    public ThreadSafeObjectB()
    {
        var num = 0;
        DoThing = () => num = 1;
    }
    public readonly Func<int> DoThing;
}