Is it safe to start a new thread in a BroadcastReceiver?

Is there any risk that the process will be killed before the thread is done?

If this receiver is registered via the manifest, yes.

If this receiver is registered via registerReceiver(), the lifetime of your process will be determined by other running components.

Is it better to use an IntentService instead?

If that work will be over a few milliseconds, IMHO, yes, probably in concert with WakefulBroadcastReceiver.

Any other better approach?

There is a goAsync() option on BroadcastReceiver that gives you a window of time to do work in another thread before triggering an ANR. I avoid this, because it is poorly documented. For example, it does not directly address your question: what is the process importance while this background thread is doing its work? Does this keep the device awake long enough for our work to get done? And so on. I'll use an IntentService or some other form of Service, where I have better understanding of the contract.

It isn't the best idea. The life-cycle of a BroadcastReceiver lasts as long as it takes to finish calling onReceive(), after that it's destroyed. If you were to start running a new thread, there's a chance the BroadcastReceiver would be killed before the thread completes, which would wind up in some unexpected behaviour.

The better option would be to start a background service, like you said.