$('.' + container).hover(function() {
        t = setTimeout( function(elem){
            //this should be executed as long as I hover,
            //with interval declared in viewSpped variable
            $(elem).find('img').first().appendTo('.' + container).fadeOut(500);
            $(elem).find('img').first().fadeIn(800);

        }(this), viewSpeed);


    }...

t = setInterval( function(elem){
        //this should be executed as long as I hover,
        //with interval declared in viewSpped variable
        $(elem).find('img').first().appendTo('.' + container).fadeOut(500);
        $(elem).find('img').first().fadeIn(800);
    }, viewSpeed, this);

var $elem = $(this);
t = setInterval( function(){
         $elem.find('img').first().appendTo('.' + container).fadeOut(500);
         $elem.find('img').first().fadeIn(800);
}, viewSpeed);

$('.' + container).hover(function() {
    var self = $(this);
    t = setTimeout( function(){
        //this should be executed as long as I hover,
        //with interval declared in viewSpped variable
        self.find('img').first().appendTo('.' + container).fadeOut(500);
        self.find('img').first().fadeIn(800);

    }, viewSpeed);
}...

var elem = $(this);
var container = $('.' + container);

t = setInterval(function() {
        elem.find('img').first().appendTo(container).fadeOut(500);
        elem.find('img').first().fadeIn(800);
    }, viewSpeed);