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