Easy to solve: either add a programmable t-stat, or you can add a vent-less gas wall heater to bring the temp up quickly and cheaply, then let the electric take over on "cruise control". 

Where are companies typically lacking in resources that they’d be willing to bring on a part time person?

In slow times, sure bring a bunch and let them do business and fight for the sale.

Rent $1200-1400 won't bring much cash flow on $250K property, it's better to cash out the equity

.— (1) Without regard to any other remedy or relief to which a person is entitled, anyone aggrieved by a violation of this part may bring an action to obtain a declaratory judgment that an act or practice violates this part and to enjoin a person who has violated, is violating, or is otherwise likely to violate this part.(2) In any action brought by a person who has suffered a loss as a result of a violation of this part, such person may recover actual damages, plus attorney’s fees and court costs as provided in s. 501.2105.

Despite its small size, the associated expenses--especially if you hope to add in a loft, address sewer/septic needs, and bring it up to code--may be significant.

Thanks for bringing that up though.  

or a rule of thumb on how much money needs to be injected into a home to bring an outdated home to sparkling brand new (this wouldn't include foundation or structural issues)?

Figure out what knowledge and experience you plan to bring to the project and what role you plan to have.

@Marcus Auerbach the deal turned out not to be a good deal Afther all, the home needed 85,345 in work that’s including an addition, to bring the value of the home up.