How can I prevent my Desire HDs battery from draining overnight?
I'm suggesting an app called PowerTutor (free on the Market). When you turn on the profiler, the app monitors the power usage of each applications and android subsystem, and give a detailed report of what application has been consuming the most battery. 

The idea is, you turn the profiler on, then use the phone as usual. Be aware though, the power profiler itself is very power-hungry and it does not save the profiling result if the profiler is restarted, that means if your phone's battery runs out before you can look at the report, you'll just be wasting battery (IOW, you might need to wake up in the middle of the night to look at the report before your phone runs out of battery; or you might need to put the phone on charger, which might affect the result of the profiling since some applications might behave differently when charged and when on battery).