Ok so with a sting there are a couple of processes going on. First there's the initial pain response, then there's activation of inflammation leading to swelling.
1. Pain. Pain signals are transmitted through nerve fibres. There are many different types of fibre which transmit at different speeds.
Typically in these sensation pathways, once sensation is detected the signal is passed between 3-4 nerve cells to reach the brain. However, once activated there is also a system causing a negative feedback loop to dampen down the signal so the pathway isn't constantly sending the signal unless the 'sensor' is repeatedly triggering.
Often the same sensor and signalling fibre networks that do touch/non-painful stimuli have a higher threshold which results in a pain signal being sent.
When pain activates this pathway, it typically overrides this negative feedback loop so the pain signal keeps going.
However, over-stimulating the area with a non-painful stimulus (potentially heat but often rubbing) can lead to transmission of touch type signals which leads to the negative feedback loop being reactivated, which acts to dampen down the perception of the painful stimulus.
This is why people will instinctively rub a sore area such as a sting. This brings us on to the second part of the response:
2. Local inflammation. It's possible that these heat based methods do something on this pain gating system but that does not explain the other part of the response, local inflammation- usually leading to swelling. If these devices lead to reduced swelling then something else must be going on (either as well as or alternatively to the first point).
The injection of venom leads to activation of inflammatory signalling pathways. This involves many signalling molecules and proteins. Ultimately this results in some or all the five parts of inflammation - heat, redness, swelling, pain and potentially loss of function. This will vary with the individual's response to the sting. I would hazard a guess that, if they're doing anything, the heat of these devices may also be interfering with the inflammatory signalling as well as the venom.