As a big tea drinker, my solution to this when I've been on long road trips has been to use a car-outlet-powered water boiler (the coil kind). You can get them on Amazon for under $10 and they work alright. Though it's hard to do without a passenger unless you're willing to pull over and wait 10 minutes for the water to boil. And where I've driven (up the 15 from Los Angeles to Montana), there are somewhat-frequent Starbucks, though I like my own tea better.

Carry your own tea bags or loose with a filter and ask for hot water.