Does the 2011 Altima come with a tranny cooler? Should I install one if not?

Probably. The gen4's through (I think) early '10 came through without coolers, but if it had a warranty tranny failure there's a good chance it was retrofitted with an OE radiating cooler. There was a bulletin for them:
https://static.nhtsa.gov/odi/tsbs/2014/ ... 3-6508.pdf

An '11 should have a heat exchanger. Just inspect the beehive, if it's a 2-port then it has no cooler and you should add one.

Just replaced the radiator. The radiator had 2 small hoses attached to it. Are those hoses what cools the tranny?

Yep. There's a mini radiator-inside-a-radiator on the other side of those fittings. They're always in the outlet tank, so they dump tranny heat into coolant that's already passed through the radiator. That's usually 25~40F cooler than the nominal thermostat temperature, and heat transfer from fluid to fluid is roughly 27 times more efficient than fluid to air. So it doesn't take a very long tube to have the same effect as a large radiating cooler. Problems only enter the picture when the cooling system is stressed and the tranny is loaded, then the outlet tank temp rises at the same time the tranny is heating up and the exchanger loses most of its cool.

So do you recommend that I install an aftermarket transmission cooler? Car has 205k miles and I want to make it last as long as I can.

Depends on the sort of driving you do and the climate where you live. The heat exchanger works well under most normal circumstances. It's only when the cooling system is stressed and the tranny has a load that a radiating cooler will help, like climbing steep hills or mountains in summer heat. Of course it's also cheap insurance against an overheated engine, which will overheat your CVT too. Not to insert a shameless plug, but you might want to consider this gizmo that I just got done developing, with or without a secondary cooler.
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