This technique may put a little more accountable on the tenant to repair it if it ever malfunctions as they understand that they are paying for it and asked for it.

I find it more favorable to have tenants bring their own microwaves, allowing them to handle any potential malfunctions.

I am sure that the air conditioning unit which was a heat pump was malfunctioning but they never fixed it properly. 

Mind is malfunctioning right now...

For example, my lease requires under the "Maintenance" section, among other things, that the "Tenant shall immediately notify Landlord, in writing, of any problem, malfunction or damage." 

If not and you have a pump somewhere in the system it could be malfunctioning and that would be a reason for the frequent pumps.

The lease should also list who is responsible for maintaining the equipment in the event of malfunction, i.e. automobile lifts breaking down.

Is it possible it was a malfunction of the thermostat/heating system or did the upstairs tenant really turn the temperature down so low that the pipes froze?

That will get them moving.Also, background and credit check, security deposit, Work information, previous residence information, Fix the house once, after that, "you break you fix" or "reasonable repairs of malfunction" (like roof leak or plumbing issues), have them sign it-- take pictures of the house before then tenant moves in, and take out of security deposit, based on the pictures you get when they are leaving --  you were too nice.   

The Seller did sign and give us a Residential Property Condition Disclosure where it was stated that the Seller was not aware of an defects/malfunctions in the central heating.