A good starting point is to look at The Health and Safety at Work Act 1974 and related statutory instruments, which impose a general duty on employers to ensure, so far as is reasonably practicable, the health, safety and welfare at work of all their employees. This includes a duty to undertake risk assessments and manage activities to reduce the risk factors. In addition, under common law an employer owes a duty of care towards its employees, the breach of which can amount to negligence.
The issue is how far is an employer expected to go to achieve this. Humans may have various different sensitives or issues which may be affected by a wide range of variables in the working environment and it may be impossible to ensure that everyone is not affected in any way. There will be obvious risk factors but air conditioning is unlikely to be one of them as millions of workers work in such environments without any issues. So this is clearly a more individual problem than a clear health and safety risk that can affect the workforce in general.
That does not mean the employer cannot be expected to do anything about it and of course there will be a duty on them to try and deal with it as best as possible. They cannot be expected to withdraw the air conditioning in general so it is about what is available and feasible. This could be placing you in an office which does not have AC, allowing you to work from home, etc. However, if there are no offices that have no AC and it is not practical to create one then they cannot be expected to do this. Similarly, whilst working from home can be an option it would depend on how practical that is and if your work will be affected by it.
Your rights will also depend on whether you are classified as disabled under law (it does not have to be a physical impairment for this to apply) and in that case the employer will have a strict duty to make reasonable adjustments.
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