What is the time constant as that 60K heat pump warms up? Would it ever
reach steady state and a COP of 3? Well maybe when it was running after
the setback period ended.

60,000 steady state heat output, 20,000 load each hour hmm, wonder how
many times that will cycle on and off drawing LRA? Well if a dog year
is 7 years, a Nick year must be 3 years.

Maybe assume it takes 15 minutes to stabalize and work backwards from
there for your time constant.