Setting the temperature
As a heat pump is 300% more efficient than a gas boiler, how instant is the heat produced by comparison?
For example, if I set my room thermostat to 21 degrees where the room temperature is currently 17.5 and outside is 0 degrees, it will take two hours to get up to 21 degrees.
How long would a heat pump take?
I think the only answer anyone could give is, 'it depends'. Not very helpful I know but there are just too many variables that will be specific to your installation. For example, how big is the room, is it underfloor heated or radiators? Is the floor carpeted? How well is the house insulated? All of those will have a bearing on the answer to your question.
My house is a new build, designed specifically to work with an ASHP. There are five zones (rooms) downstairs all heated by UFH and individually controlled by a thermostat in each zone. Upstairs is all radiators, and these are controlled by a single thermostat on the landing, and each radiator having a thermostatic valve.
The largest zone is the open plan kitchen, dining and living area. For me, if I wanted to bring this room up from 17.5 to 21c I'd expect it to take 3.5 hrs (about a degree an hour) and this can use 25kw upwards. But, the pay off is that once its at temperature, the floor retains heat for ages, keeping the room warm. I've been in a year and it's been a bit of a learning curve having to get used to a new way of heating the house. If the room temp drops too much, the ASHP uses a lot to get back to temp. I've found that leaving the thermostats set to say, 20c with maybe a drop of 1c over night is a much more efficient way of heating as the ASHP does not use as much power to keep the temp 'ticking over' than it does to recover from a large drop in room temperature. This does mean that the ASHP will kick in for short periods overnight but I've found that this uses far less power to keep the temp constant than it does if I set the overnight thermostat to a very low level.
These are just my observations though. I'm no heat pump expert, just a consumer.
After a year of use, I'd say that overall the ASHP has been cheaper to run in my larger new 2022 build detached than the old gas / electric combination at my old 1980s built detached house based on my back of a fag packet calculations applying current energy costs to my bills at the old house.
Sorry I haven't answered your question directly, but hope you find my experience useful.
The temperature of the internal circulating fluid is the main part of the equation. The higher the temperature, the faster your property will heat up. But the efficiency of your system will reduce as you increase the temperature.
If you use the same temperature as your current boiler it will heat up at the same rate. You could tinker with the temperature of the boiler and try it yourself. Our gas combi boiler circulates at 50c at the moment and it's fine all year round. The return temperature is around 35c and we use a minimum thermostat temperature of 18c so the house never gets cold.
We don't have a heat pump yet but I've been tinkering for a few years adding radiators and underfloor heating in anticipation of getting one so the temperature of the circulating fluid can be quite low.