Well... I haven't received a tank in two years, but they probably haven't changed that much. They're huge. Like 1 foot across and deep, and 2-2.5' high. You couldn't fit one in a fridge if you tried. And it's not necessary. I don't know the science behind it, but those suckers stay cold for at least 7 days. Closer to 14 really, but Northwest won't guarentee them past the 7 day mark.
Good luck! And.. you said that you plan to use the vial when you get your smiley.. you mean a little after, right? The smiley is indicative of your LH surge, which is before you ovulate.. you probably already know all that, but just in case you didn't... the younger you are, the further from your LH surge you ovulate (up to 48 hours or so), and the older you are, the closer to your LH surge. When I was 27, I insemed at around 19 and 32 hours. I'm just a few years older now, and I'm going to try for 12-24 this time (based on other signs telling me I'm ovulating closer to Zero Hour (aka positive smiley and LH surge). Good luck, and happy baby dust!