It's difficult to give a pressie length of time it will take for a caravan to warm up as there are lots of factors that will affect process in the real world.
Years ago I was involved with testing of caravan heating, and the procedure we used was to take a caravan and place it in an automotive environmental chamber which could control its temperature anywhere between -15C and +50C, A series of thermcouples would be positioned throughout the caravan and connected to a multipoint recorder.
All the caravan doors, windows cupboards and seats would be opened up and without the heater running, it would be cooled for at least 12 hours to +5C. When all the thermcouples were showing +5 (+/-0.5C) the caravan would be closed up, and the heater started.
The time it took for the combined average of the thermcouples to reach 20C was one of the important outcomes.
Having tested both wet and dry systems, there were certain characteristics of each type of heating that became apparent.
Here are a few generalised notes and comparisons:-
There are fundamentally two aspects of creating a comfortable warm environment, air temperature and material temperature.
Air is easier to warm up than solid or liquid materials. It's therefore easy to understand that a blown hot air system will warm up the volume of air quite quickly, but the fabric of the space may still feel cool to the touch. It will take some time for the warm air to transfer enough heat to the fabric of the caravan to make it all feel warm. Specifically in the case of caravans and motor homes, the blown air systems vents direct hot air into the living spaces which mean the volume of air in cupboards and bed lockers are not heated directly. This means the living space air will warm more rapidly than beds and other enclosed spaces. The fact the air is also being forced to move tends to mix it up more reducing the natural tendency for air to stratify becasue of its temperature dependant buoyancy.
By comparison, wet systems tend to have convection points often behind bed/seat backs, or dedicated radiators typically in bathrooms. The majority of heat is liberated by convection, and will immediately rise and collect at the top of the caravan, but it will also be heating more of the structure of the caravan as it does so and more of the enclosed space not part of the living area. This will mean the air temperature will increase more slowly, and becasue its not being forced to mix, it will also tend to stratify more with a bigger temperature difference from top to bottom.
I summaries the initial warming characteristics of each system as blown hot air warns from the core outwards, whilst the wet systems warm from the outside inwards. Which is most beneficial to the users can depend on how active you are. For instance if you are standing up, then you will benefit more from air temperature, but if you are sitting then your contact with the furniture will have a significant influence on how comfortable you are temperature wise.
Longer term after a about three hours or so the difference of the systems is less marked. and other factors start to have a bigger influence. The length of a caravan will adversely affect a blown air system more than a wet system for even heat distribution.
Wet systems take longer to recover lost heat when the door/window is opened.
Even though the individual components of a heating systems are manufactured to close and consistent tolerances, and are inherently reliable, Both wet an dry systems are adversely affected by poor design and assembly of the installation by the caravan manufacturers. Often cost cutting means less than optimal systems are installed.
In practice, there are other factors that also influence the performance of a heating system, For example Wind and Rain will strip heat away from any surface it falls on. the addition of an awning will reduce heat loss from that side of the caravan, by keeping the wind away, and possibly helping with a little insulation.
Humidity not only affects how quickly a volume of air will heat up, but also affects the feel and comfort. Each living being simply breathing (Approx. 200ml per person per day) will raise the level of humidity inside a caravan, and that not only affects the air but also the wood and other soft materials in the caravan which will absorb moisture, and can also be seen as condensation. Any open flame (hob and oven) or near boiling water will also raise the level of humidity.
By the same token sunshine will warm any surface it falls on, and of course sunshine entering through a window will also assist with heat gain.
So when you delve into the science behind it all it looks complex, but empirically blown hot air will warm the air in a caravan more quickly, progressively wet systems will catch up and after about 2 hours or so the differences between correctly set up wet and dry systems is barely worth mentioning.
This is all based on similar sized and constructed and used caravans.
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