Yes, you can.
In fact, this is a specific technique known as a " coffee toddy " which is a good way to take liquid coffee camping with you if you don't want to take brewing equipment.
Some people even prefer coffee made this way to other methods of brewing.
cooking.stackexchange.com/users/7180/FuzzyChef
Yes.
Coffee gets its flavor from a number of compounds such as oils, which can break down at high temperatures.
But this takes time.
As long as you drink the coffee before it gets stale, heating it should be fine. Also, caffeine is quite stable at hot-coffee temperatures.
cooking.stackexchange.com/users/8320/JSideris
Heating didnt work for me.
I tried this today.
Yesterday I soaked a tsp of illy in water for 24 hrs.
It came up quite good.
Not very bitter.
I filtered it and heated it on very low heat, (a setting of 3 out of 6 on my hot plate) until it started to give off a little steam.
Now it felt quite bitter on tasting.
I always make my hot coffee in a moka on this temprature and its doesnt burn, So I dont think I burnt my cold brew
cooking.stackexchange.com/users/1890/Midhat
My experience of heating coffee in a microwave is very negative, although I cannot explain the mechanism for it turning out so awful.
It may be the effect of the hot coffee cooling down, rather than the effect of the reheating.
We've all experienced coffee that's been sat on the hotplate for too long; bitter and acrid.
You risk this "burning" effect if you heat cold coffee on a hotplate.
Cold press coffee is generally brewed very strong indeed; about twice as strong as espresso.
Hence you can add boiling water at a ratio of, say, 3:1 and have an acceptably warm cup of coffee - and this is what people usually do.
If you want to microwave for extra heat, just microwave the full-strength cold-brew for 10 seconds or so, before adding water from the kettle.
cooking.stackexchange.com/users/4214/slim
Cold brewing and storing in the fridge can be done with an Aeropress without loosing flavor.
This thread talks about both cold brewing and keeping it in the fridge: http://coffeegeek.com/forums/coffee/machines/432108
cooking.stackexchange.com/users/5981/homaxto
Apparently keeping coffee hot and reheating it both lead to bad flavors:  How can I reheat coffee without imparting bad flavor?  Why does coffee taste awful after reheating it in a microwave oven?  However, can you cold-brew coffee and then heat it (microwave or other) without ruining the flavors?  If so, why?
Can cold-brew coffee be heated? Why?
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<coffee>
cooking.stackexchange.com/questions/19777
cooking.stackexchange.com/users/7691/keflavich
This technique is called a 'coffee toddy' and is good for camping without coffee making equipment. The coffee and caffeine in it are not harmed by the heating process. Cold press coffee is generally brewed very strong indeed; about twice as strong as espresso, so you can heat it in the microwave for a few seconds before adding hot water. If you want to heat up cold brew, then microwave it and add boiling water to dilute.
The coffee toddy is a technique for reheating coffee when camping. Cold press coffee is much stronger than hot coffee. You can microwave then add boiling water to dilute it to the correct strength.