Well, I'm going to assume your softener is before the only point of entry for your house water supply. As such, no, I doesn't make sense to me. I think I would start looking for a stoichiometric answer. Your water isn't harder I don't think, but I do know that when I measure specific gravity during wine making there is a temperature variance that you have to account for if the must or wine is hotter than 60C. So, it stands to reason that your test strips may need or require a differential based on temperature.
Here's a question, are you measuring out of the hot tap? What if you let that hot water cool to room temp? Same reading?
In the flip side, it's possible your soft hot water is absorbing the high hard water precipitates if any existed.