@anzah
Yes, that's advisable! You definitely don't want a tea thermos tasting like coffee.
That's actually a good idea to pre-warm the thermos, the way you would a porcelain teapot, though with porcelain it's just to prevent the shock. You could always use the warm water to do dishes or save it for plants.
And you're right, coffee is a little cooler when it comes out of the aeropress. I only do the thermos thing when I use my coffeemaker to make a whole pot.
I've tried out various little mug heaters and what-have-you, but I've never really been satisfied with any of them, especially the USB kind.