It is possible that there's an effect on beard growth from changes in temperature; but most "authoritative" opinions are just authoritative opinions in the mind of the "authority."

The more likely explanation for a need to shave more in hot weather, for most, is that when you perspire more the skin where the hair grows gets more sensitive, so you feel like the hair is longer, sooner.

If you look in the mirror and see more hair sooner after a shave, the cause more likely is that because of perspiration and the "other oilies" the perspiration brings to the skin surface of your hot skin, the previous shave just wasn't as close as you normally get, with your shaving method, when your face (or whatever you're shaving) is cooler.

In hot weather, you may get a closer first shave if you wash (soap and water or shampoo) first, then rinse with an alcohol splash. Ordinary rubbing alcohol works as well as fancy stuff for this step.

If the alcohol "burns," rinsing with cool or cold water will stop the burn instantly. (Rinsing with warm or hot water will make it burn more.) If there's a burn from the alcohol, it means that you haven't cleaned all the little cracks and holes in the skin, and by extension that you haven't gotten all the oil off the hair, so repeat the alcohol rinse until rinsing with warm water doesn't burn, so that you know that all the oilies have been removed. Repeating the alcohol rinse a couple of times is usually sufficient.

(The repeats are why using cheap propanol - rubbing alcohol - is better than using "shaving products." It's cheap.)

Once the skin and hair are "confirmed clean" you can be reasonably sure of getting a consistently clean "first shave" so that you'll be better able to tell if the beard (or whatever) actually is growing faster.

There may actually be a change in growth rate, but there also may be a need to "change your shaving habit" when the weather changes.

John