Should I burn wood with termites in it?
I wouldn't choose it over nice dry clean wood.
Wood with termites in it is more likely to be either rotten or moist, having been outside for long enough to attract the critters.
As such, it will not be a good source of heat and will likely not burn well.
In addition, if you are storing termite riddled wood near your house (and I assume you do keep your firewood within easy reach of your fireplace or woodstove...) you are running the risk of introducing them to your house itself....
Need I say more?