It is interesting to consider what happens with our thoughts while engaging in Centering Prayer. We are often told to "let go of thoughts" as or when they arise but the truth is our first consciousness of a thought is when it has already come. Also thoughts don't seem to arise but rather arrive so I am thinking of doing a new take on it.

Lets look at what happens in Centering Prayer:
1) You are in prayer.
2) A thought arrives.
It isn't static - it is already moving into irrelevance bringing in its train more thoughts.
3) By this time you have realised you have been caught up in your thoughts.
4) For that brief moment you have stopped. You have, as it were, put on the red light and said "hold it!" - If only for a split second.
It's that split second that matters.

What do you do?
There are no thoughts to "let go of" - they've gone further down the line
There are a whole lot more potential thoughts waiting at the signal.
You know if you relax for one second they'll come rushing through.

What to do?
The key is to remove the tracks further down the line
It is not the thoughts that are of prime significance but the fact that they have somewhere to land further down the line.
Without prepared ground they have nowhere to land - they have no substance.
As Martin Luther put it: "You cannot stop the birds flying over your head but you CAN stop them landing in your hair"
So we are not letting thoughts go but letting go of the faculty upon which they seek to find a home. So ... potential thoughts come and as our imaginary "thought train" falls off the cliff without a track to pursue its journey so similarly thoughts just fall away.

What actually do these tracks represent?
Our mental ATTENTION.
Our mental attention attends to, provides a landing space for potential thought.

ANOTHER ANALOGY
A projector and a screen.

The projector sends the light (the thoughts)
The screen attends to, receives, displays and gives substance to the light rays thus creating a picture.
If we remove the screen and simply let the light from the projector disappear into infinity there will be no pictures.
There is only a picture if there is something upon which the light can land upon.
If we remove our mental attention there will be no screen for the thoughts to find form - we may be aware of their potential back down the line. We may be aware of the projector but they will have nowhere to land here!

So we let go of our mental attention - where to?

Down to our HEART - the INtention of the heart

We let go of our attention of mind in favour of intention of HEART
That's why I say thoughts don't arise from the heart but arrive to the mind.
When our mode of reception is the heart thoughts do not find a home.
This letting go of the screen. This taking away of the railway line is the kenotic activity with which we are to engage as soon as we sense a thought stream on its way to our present.
Not the letting go of thoughts but the letting go of the attention with which they find a home will ensure greater repose than the frenetic business of dealing with "each thought as it arises".

ANOTHER ANALOGY

The tennis ball machine!
Imaging thoughts like tennis balls being fired at you from a machine. You can catch them if you like as they come - that is the equivalent of the thinking mind taking to itself every thought that comes its way.
Alternatively you can refuse to catch them but your hands are still at the front and somewhat open and you just cannot help catch the odd thought untill eventually you are catching all the tennis balls again!
The other alternative is to put your hands behind your back - it is then impossible to catch the balls - to grasp the thoughts - What we are doing here is putting the mind behind the heart - Giving the heart priority in all our dealings - the prime interpreter of reality. Hence the term "Heartfulness". The mind in its turn will receive its information form the heart rightly interpreting events as they come.