The fear of god isn’t enforceable. The main thing you do in referencing OSHA is to demonstrate a level of knowledge, commitment, or at least interest in the issue. And most of the time it is the appearance of concealing a condition that is the enforced violation. This is usually what companies are actually sensitive to.
So while an OSHA violation is a serious thing, the conditions in question here (heat) are not a regulation that can be violated and therefore enforced in the same way.
I get what you mean, and it’s a common thought and strategy. It just doesn’t work as well as one might think. Unless there is a union, employees are at a significant disadvantage. Forming a union would be FAR more effective than quoting OSHA regs.
The main thing is regulatory violations aren’t (usually) criminal so there’s a long administrative process to most enforcement actions. Companies overwhelmingly have the resources to litigate beyond their employees means. So if they have the resources to have legal council or a compliance officer, there likely needs to be a well documented paper trail of concealment or otherwise flagrant disregard or denial of improved conditions.
There not being A/C isn’t enough. Refusing requests to install A/C is better. The company removing workers fans to make a point goes further in a case. Then putting out an internal memo requiring zero ventilation and to lie to investigators is a strong case.