Teant's obligation is to pay rent. Landlord's obligation is to provide liveable housing. In US law the legal concept is that the lease has "implied warranty of Habitability". That is to say landlord should gurrantee the house is liveable (habitable).
Being habitable includes water/plubming, electricity, heating/cooling, etc. Landlord has no general obligation beyond this, unless the lease specially provides (such as lawn mantainance / snow removal etc).
Therefore, as long as your thermostat works, there is no obligation to change to a new one. As long as the house is clean enough for normal people, there is no obligation to specially clean for a person with allergy.
This is what major apartment company do. They won't spend money on these issues you mentioned. The only reason the tenant is asking you is because you are small landlord and you are not as nasty as the property manager at major apartment buildings.
Now you know the bottom line, whatever you decide to do is up to you. You can say no, say partial yes, say you pay for everything. Each choice has its pro and con, I don't think you need me to explain.
