I've never used WTF, so can't comment on that. Obviously "thickness" of the CA will be the most important factor in cure time. Not all "thin" and "medium" CA are created equal. My understanding is that CA is generally ethyl 2-cyanoacrylate and the thickness is determined by how much "thickener" is used, methyl methacrylate (the monomer for PMMA or plexiglass) is one thickener that is used. For example, I use Bob Smith Industries CA and their Thin CA has no methyl methacrylate, Medium has about 5% and Thick closer to 10%. Interestingly, when CA is modified with methyl methacrylate it has slightly different properties, it is less stiff and has better impact resistance, but I digress. The age of the CA will also play a role. My understanding is that there are two major contributors to reduced activity of old CA: 1.) gradual polymerization of the CA results in a more viscous liquid with less reactive, longer chain molecules, and 2.) water in the CA will slowly react to form acids that are not neutralized when the CA is exposed to ambient conditions, this acid inhibits the polymerization reaction. There are also a whole slew of inhibitors, stabilizers, and viscosity modifiers that are added to CA adhesives intentionally to change their properties, each brand/product will respond slightly different in the conditions in your shop and the exact application.
After composition, I would argue that temperature is probably not the most important factor when finishing pens. Humidity plays a more important role, but as you would expect higher temperatures generally mean higher humidity. Water consumes the acidic inhibitor in the CA which allows the polymerization to occur rapidly. Without any water (humidity) the inhibitor remains in the liquid and no polymerization can occur (like what happens in the storage container). This is why the manufacturer recommends not storing the CA in a refrigerator after it has been opened, the heat cycling forces humid air in the container and degrades the CA.
Next, the substrate plays an important role. I notice that the first couple coats of CA cure very fast, but the substrate is wood and the CA chain reaction is initiated by the moisture in the wood. After that the subsequent CA coats are on top of prior CA coats, so it needs to search for moisture in the air to cure.
As for temperature, Cyberbond states that the rule of thumb for temperature is that cure time halves with each 10 degC increase in temperature and the ideal is 20 to 24 degC. Therefore, you can expect it to take about 4 times longer to cure at 32 degF versus 70 degF (pretty sure I'm never gonna work in a shop that is below freezing...). One approach might be to add heat to the blank prior to applying CA by using some good old friction, then you don't need to heat up your entire shop. But it is my opinion that increasing temperature alone probably isn't going to significantly change the cure time (or amount of time needed to finish a pen).
The moral of the story is "its complicated". If you think your CA is bad, buy some new stuff or change brands. If you think its too dry, use some accelerator. If you think its too cold, wait a little longer...