Discussion doesn't seem to be really widespread, but particularly with the M.2 / PCIe SSDs you actually do get some thermal throttling. Here's a review of the Samsung SM951 where in just over 2 minutes of sequential write testing the card reached a throttle temperature of 82C and throughput dropped from 1500MB/s to 70MB/s (http://www.legitreviews.com/samsung-sm951-512gb-m-2-pcie-ssd...). I'd call that a noticeable dropoff in speed. Yes, I realize that article is talking about SSDs not SD cards. The relevant difference here is that the SSD is substantially larger with likely better heat dissipation.
Of course, the maximum bus speed of SD cards right now (including the UHS-II hardware change to add additional contacts) is only ~300MB/s, with a more practical top speed of ~150MB/s to allow both reading and writing. Maximum power consumption of UHS-II SDXC cards is 2.88W, which is actually fairly significant when you consider the volume of the cards - it's not a lot of power, but it's also not a lot of thermal mass.
Of course, the maximum bus speed of SD cards right now (including the UHS-II hardware change to add additional contacts) is only ~300MB/s, with a more practical top speed of ~150MB/s to allow both reading and writing. Maximum power consumption of UHS-II SDXC cards is 2.88W, which is actually fairly significant when you consider the volume of the cards - it's not a lot of power, but it's also not a lot of thermal mass.