Script that updates images on the cart page to show the correct thumbnail as chosen in the Variant Images app.

variant-images-in-cart.html

{% if cart.item_count > 0 %}
<script>
// Script that updates images on the cart page to show the correct thumbnail as chosen in the Variant Images app.
// This works with any markup.
// This works when using Line Item Properties where several items in the cart form can share the same variant ID.
// Author: Caroline Schnapp.
// Place at the top of your cart.liquid template.
(function($) { 
  var variantImages = {},
    productHandles = [];
  {% for item in cart.items %}
  productHandles.push('{{ item.product.handle }}');
  productHandles = $.unique(productHandles);
  if (typeof variantImages[{{ item.id | json }}] === 'undefined') {
    variantImages[{{ item.id | json }}] = [];
  }
  variantImages[{{ item.id | json }}].push({{ forloop.index0 }});
  {% endfor %}
  jQuery(function($) {
    $('form[action="/cart"]').each(function() {
      var images = $(this).find('img[src*="/products/"]').hide();
      var size = images.first().attr('src').match(/thumb|small|compact|medium|large|grande/)[0] || 'small';
      for (var i=0;i<productHandles.length;i++){
        $.getJSON("/a/variant-images-1?shop=" + Shopify.shop + "&handle=" + productHandles[i], function(data){
          $.each(data, function(variantId, image) {
            if (typeof variantImages[variantId] !== 'undefined') {
              for (var j=0; j<variantImages[variantId].length;j++) {
                var oldURLParts = images.eq(variantImages[variantId][j]).attr('src').split('?');
                var suffix = '?' + oldURLParts[1];
                var prefix = oldURLParts[0].split('/');
                prefix.pop();
                prefix = prefix.join('/') + '/';
                var filename = image.filename.replace('.', '_' + size + '.');
                images.eq(variantImages[variantId][j]).attr('src', prefix + filename + suffix).show();
              };
            }              
          });    
        });
      }      
    });
  });
})(jQuery);
</script> 
{% endif %}

I actually managed to change the product featured image shown on cart page with the variant image by editing the code in cart-template.liquid
Search for image: item.product.featured_media.preview_image and replace with image: item.variant.featured_media.preview_image

I am still checking where can I do the same trick on the mini side cart.