public class MyDict : Dictionary<MyClassKey, MyClassValue>
    {
    }

    public class MyClassKey
    {
        public string Str { get; set; }
        public DateTime Date { get; set; }
    }

    public class MyClassValue
    {
        public string Str { get; set; }
        public DateTime Date { get; set; }
        public int Value { get; set; }
    }

var list = new List<MyClassValue>()
            {
                new MyClassValue()
                {
                    Date = DateTime.Now,
                    Str = "Hello",
                    Value = 1
                },
                new MyClassValue()
                {
                    Date = DateTime.Now,
                    Str = "World",
                    Value = 1
                },
            };

            var temp = list.ToDictionary(x => new MyClassKey() { Date = x.Date, Str = x.Str });
            MyDict myDict = temp;  << Ошибка компиляции