I suspect the author has come to this conclusion from CGM data, and therefore also that it is wrong (or at least not a very significant effect).
I also have T1D, and CGMs like Freestyle Libre (and probably also Dexcom) includes a temperature sensor and adjusts its readings based on the external temperature to increase accuracy. I think the changes in blood sugar levels during hot showers (etc) is probably due to the sensor not adjusting quickly enough to the rapid change in temperature, and not a physiological response.
For example, if I go directly from room temperature to my cold balcony, the CGM value will immediately make a huge jump upwards with the next reading, but then quickly revert back down again within the following readings. Considering the 15 minute lag time between plasma glucose and the interstitial readings of the sensor, its unlikely the sensor is immediately measuring a change in plasma glucose – it's simply (over)reacting and adjusting to the new temperature (since the thermometer won't have such a long lag time).
Very hot environments, such as a hot sauna, also makes my CGM readings completely inaccurate.