Things that I have come across that created similar ish symptoms
Copper wire in HT lead near spark plug corroding (green verdigris) can't think why it would work after a rest.
Water in fuel - pooling in the bottom of the filter (which is horizontal) and building up so that it is getting through to carbs. Normally the fuel would flow over the top of a small amount of water. Stopping, cooling snd pressure changes may alter the level of water. Suggests a pool of water in the bottom of the tank.
Carb vacuum tubes cracked / split. The symptoms sound like mine behaved when one hose detached at the lower end after its first garage service. A cracked tube may be more prone to let in air when the tube gets warm and seal up when it cools off a bit.
Dodgy fuel pump relay contacts. Switch it with a headlight relay.
(Does the ST1100 have a fuel pump relay ? Not such a stupid question if you read the technical bit below.)
All the above suggestion fall into the 'clutching at straws' category. The suggestion below falls into the 'clutching at thin air category', but since I came across this one day and it intrigued me, I worked out how it worked.
Basically, there is an electronic device on the ST1100 that detects when the engine is not running and turns off the fuel pump.
It turns on the fuel pump every time there is an ignition pulse. There is a delay circuit which turns it off if a new ignition pulse doesn't turn it in again. So the fuel pump is always turned when the engine is running, but it is always in the process of being turned off after each ignition pulse -there is a time delay to it being turned off which means it should not get turned off before the next ignition pulse.
I cannot remember whether it does this directly, or whether a fuel pump relay is involved.
My attempt at a technical explanation - from memory. There is a device that keeps fuel flowing while the engine is running. It is turned on by a silicon controlled rectifier - SCR. Basically it is a diode with an extra control lead. Electricity doesn't flow through it until it is turned on, which will happen as soon as it gets a single pulse of power on the extra control lead. Electricity flows through the diode, once it has received a pulse on the control leg. It turns off if there is no power on the positive leg. You can turn off an SCR by momentarily attaching the positive side to earth, or by shorting the positive and negative legs, by-passing the SCR.
I think that this device is used to control the fuel pump relay. Although it could be used instead of a fuel pump relay.
The coil input is firing up to 18000 times per minute. 300 times per second.
That quick pulse repeatedly turns on the SCR which turns on the fuel pump.
The positive leg is permanently attached to earth - but through a capacitor and relay.. That combination provides a time delay before the SCR positive side is fully connected to earth and the SCR is turned off. The intention is that the delay is longer than the time it takes to get another ignition pulse to turn the SCR on again.
The engine runs at say a minimum of 600 rpm. So that is 20 ignition coil pulses every second. One every 1/20th of a second
So the SCR is turned on every .05 of a second, and it will stay on until the input is connected to earth
But The capacitor / resistor drains will connect the positive leg to earth after a time delay. Say after half a second.
The regular pulse from the ignition coil keeps the SCR, and therefore the fuel pump, turned on.
If it doesn't receive another pulse, then the resistor / capacitor combination will turn off the SCR within half a second (say)
It is a safety mechanism so that if the engine stops, the fuel will turn off. While the engine is running, it stays on.
But if that time delay mechanism breaks down and is turning off the fuel pump before it gets turned on again by the ignition pulse, then the fuel pump motor may not be running as it should. It could be being turned on and off very rapidly.
Why would this be affected by heat ? If you read the italicised bit, you will see that the electronic device is dependent upon a resistance, and resistance is affected by heat. Also by corrosion and dry soldered joints. It may be causing the fuel pump to turn off and in at a rapid rate, rather than keeping it in continuously.
I'm sorry. I do not know where this device is or what it is called. I came across it a few years ago as a circuit diagram and I worked out what it was doing. The ST1300 doesn't employ the same technique. But having described its behaviour, someone else may know what and where it is located. Basically it is an electronic fuel cut off switch.
