Great question! I know for sure because the picture is from a couple of weeks ago and by now it's clearly a flower spike.

I had your same question when the growth was at the stage shown in the picture. I looked up how to tell the difference between flower spike and root. What I learned was that two signs of flower spike are:

• Located right below the middle of where a leaf attaches to the stem, because that's the location of a node that can become a flower spike. Roots can come from a greater variety of locations around the stem.
• Shaped like a mitten, in other words the growth is slightly asymmetric. I believe the thumb is a forming node and the fingers part is where the spike will continue growing. The mitten shape is not present in this image, it developed a day or two later. In contrast, a developing root is fully symmetric/round.

There may be other signs too or these may be incorrect, please share if you know them!

I haven't ever gotten them to re-bloom on purpose. I just keep them around for years and periodically they do. Some re-bloom much more often than others. I got a few orchid books out of the library recently to take a more informed approach. It seems like many different factors can influence re-blooming and that it depends on the genus/species. Temperature changes like you mentioned, also day length, amount of light, even pressure changes with the weather! Good luck with your orchids.