SC makes valid observations as to the problem in Dubai and if the external temperature is in excess of 30C, but the problem that is trying to be addressed is the typical UK summer day at LHR. The problem is that an aircraft will come in from a longhaul flight and will be at a reasonable temperature. IF it remains on stand AND pre-conditioned air is put onto the aircraft immediately and remains on for the duration of the turnaround then the temp will rise a little, but it is essentially not a major issue. However, if the same aircraft is not immediately attached to the PCA which then stays on for the duration then the aircraft will start to heat up. It will heat up to well in excess of the ambient temp.
Closing the blinds, and turning off unnecessary electrical equipment such as the IFE etc will slow down this temperature rise. PCA and indeed the APU struggle on a summers day to cool an aircraft, but can cope at maintaining a temperature. However, BAA will not allow the APU to be run for protracted periods of time - even if it were allowed it would require an engineers prescence all the time it was running. The PCA often does not get attached or is not available on the stand in use or the aircraft will be moved to another stand prior to the next departure.
So while closing the blinds is not a cure for the sun heating up the aircraft, it can help to minimise the temperature rise, at no cost to the company. It produces no noise pollution and emits no CO2, it burns no expensive fuel. It is certainly not a panacea, but it is far better than doing nothing and then having to do more to reduce the temp in the cabin. If nothing else it makes the cabin temp less unpleasant for your colleagues when they board in preparation for the next service.
It is a perfectly reasonable order from an aircraft captain to his crew to close the blinds prior to disembarkation. It is perfectly reasonable for the company to take measures to reduce its costs by doing this. There is no risk in closing the blinds, if there were a risk then passengers would not be allowed to do this unsupervised. Refusal to do this could expose the crew to disciplinary action from the company, and over what? nothing of any import.
This has not been done as a deliberate act to provoke militants, although I do believe that BASSA are hypersensitive about everything at the moment and will, like a spurned partner, find it hard to look at anything the company do objectively.