When I have a fearful thought/anxiety I use this process of cognitive thinking.
1) What is at the core of my anxiety right now...can I pinpoint it?
2) What is the likelihood of this event actually happening? (example, have I ever had a heart attack before? house burned down before? insert own fear here)
3) Can I then form a more reasonable conclusion to calm my worry. I am healthy, I am not going to die of a heart attack. I have not left candles burning and I have working smoke alarms, the house is not going to burn down.
This process forces the more developed, rational, thinking part of the brain to function and get exercise. It then takes away the power from the primitive part of the brain that calls for the release of the anxiety hormones adrenaline and cortisol.
It takes some practice and you may need to combine this with some breathing exercises to get you calmed down enough before you can begin to think rationally-beyond the panic, but it works.
Hope this a help to somebody.
Go rational brain...down with primitive brain!
"Courage is not the absence of fear...it is being afraid, and doing it anyway!"