The thermostat of the heat pump should hold the temperature steady as long as the heat loss is not greater than the capacity of the heat pump to replace the lost heat.

IMPO

SR

"Exact" as in not varying more .1 degree f over a 24 hour period or "exact" as in not varying more than a slightly noticeable amount over a 24 hour period?

Second consideration has to do with who is doing the programing.

Also, don't expect 1-head to keep a constant temperature in multiple rooms if the space is subdivided.

IMPO

SR

Is the thermostat on an interior wall, away from direct sunlight, drafts, or heat sources like a TV? If it's in a bad location, it will get a false reading and turn the system on/off at the wrong times."

This is an excellent starting point, as placement is critical. Assuming the location is ideal, the answer to your question is nuanced. Yes, you can program your system for an exact temperature, but how well it maintains that temperature depends heavily on the type of system you have, especially in a well-insulated, smaller space like your 600 sq ft home in the Pacific Northwest.

The most common system in your scenario would be a ductless mini split. If you do not have a ductless mini split and have a central system with a standard thermostat, the key is to upgrade to a smart thermostat.