Is there any potential harm to using warm water in my sourdough starter?
I would limit the temperature of the water to around 110F.


140F is widely cited as the "Death Temperature".
At 120F the yeast is at it's "injury point" meaning you are harming the yeast, but may not kill it.
Some claims can be found stating water temperature as high as 95 can produce off flavors from the yeast when making bread. However, this really won't apply to your starter since it will make up such a small percentage of the loaf.


Here is a relevant, although not duplicate, SA post asking when eyast is killed: What temperature of water will kill yeast?

Some sources to skim through on the topic:


http://www.homebrewtalk.com/showthread.php?t=67272
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC232826/
https://www.exploratorium.edu/cooking/bread/yeast_temp.html
https://www.reference.com/science/temperature-kills-yeast-6cd7b72a3ed2d24b