We have learned a ton and I want thousands of units one day but for now just trying what to do next with this one. ok so the issue is that home was built in 1932 and the heating is an issue in the winter and the heating costs are really high for the tenants.

They schedule leases to end in spring/early summer because they don’t want the vacancy during the winter/holidays. 

Mainly you're responsible for the sewer bill and to provide heat and hot water, but not things like air conditioning.If this was winter, I'd be concerned about pipes freezing if the relationship isn't going well, but a 10 year tenant probably won't let that happen.I don't really know about the downsides of not having a lease. 

This past winter i signed a tenant for three months with options to extend monthly until spring summer.

Very few people move out of storage in the middle of the winter and all locations around are full. 

Quote from @Marc Winter: Not sure I understand what you meant:  the TENANT wants to make a deal?

My partner bought a studio, front line to the sea in Costa del Sol, initially just a warm escape from Chicago winters with no intention to make a profit. 

My concern is being able to find a tenant during fall/winter months.

We are open for business unless there is some kind of evacuation order.This past winter there was a big snow event that the media turned into an even bigger, scarier thing. 

I remember a tenant who decided it was easier to open a window than lower the thermostat in winter.