With regard to temperature checks, these are not particularly common, so you may get push back on this. Additionally, if you are doing this, make sure the employee who takes the tests takes appropriate precautions (i.e uses a contactless thermometers, is wearing appropriate PPE, etc.). Imagine the nightmare if your test taker got sick and then got your customers sick.
There is no good reason why anyone cannot social distance from others, beyond showing an obvious mobility disability that requires someone to physically assist them in moving around. Outside of someone with a obvious disability, I think you would be well within your rights to remind the customer social distancing is required and if they continue to refuse to do so without citing any medical reason, you may ask them to leave.
With regard to wearing a mask, you may require any customer to wear a mask. If they refuse, you should ask why. Unless they say they have a medical condition of some sort, they should be barred entry. If they say they have a medical condition, you may NOT ask them for any further information. While you are required to provide them service and accommodate their disability, this does not mean you must allow them into your store. You can provide other reasonable accommodations instead. If you plan on taking this aggressive approach, I would strongly advise you consult counsel so that you can discuss what steps are appropriate and how to mitigate the risk of any blowback from customers.