In the case of temporary workers, the responsibility is shared between the organisation and the temp agency.
The DSE regulations do cover this situation in detail, although there is a table in the regs setting out the responsibility of each party. But this does leave some grey areas and the Health & Safety Manager within the organisation would usually make a decision based on what is practical.
Sometimes organisations may come to an arrangement with the temp agency about some aspects (e.g. DSE training).
The organisation is responsible for the workstation assessment but the temp agency should normally provide the training about DSE risks.
ErgoPro provides the risk assessment and the training at the same time.
Also, in practice, the organisation tends to provide the DSE training because they are the ones providing the equipment for use. But this may not always be the case, for instance if the temporary staff bring their own equipment (e.g. auditors with own laptops). The period of time that the temp is working in the organisation is also relevant because it may not be practical to provide training and risk assessment if the temp is only there for a very short period.
The temp agency would normally provide the eye test.
So in the majority of cases, the organisation will need to provide the risk assessment for a temp.