Yes, you can do something like this in LabVIEW. First you need to define the system.
Do you have an oven or chamber or does the object being controlled have embedded heaters?
What is the heat source? Electric, combustion of fuel, nuclear? How is the heat source to be controlled? Relay, thyristor, valves?
How will the temperature be measured?
How fast can the temperature change when the heat source is applied or removed? Are there any sudden changes in heat flux from the environment or load?
How accurately must the temperature be controlled? Note that accuracy and precision are not the same things.
Will the temperature profile you mentiioned be the only one or will the user have the option to change it?
How will safety issues be handled? (Valve stuck, thyristor shorted, ...)
What happens if the power goes off during the 5+ days of the run?
What data do you need to save, record, or present to the user during the run, and in what formats?
Lynn