The lime precipitation occurs well enough at room temperature. Calcium hydroxide is somewhat unusual in having an inverse solubility curve in water, meaning that it's actually more soluble at lower temperatures. I'm not sure how that shapes up when it comes to aquoethanolic solutions, nor have I any observations on what happens to the lime-treated solution on heating. It's a nuance that appears to be unimportant at present.
The reason I mention freezing is as an alternative method for concentrating the solution by freezing the water out as ice, thus conserving the ethanol content. This is in contrast to evaporation, where the ethanol preferentially gets removed. So, only freeze it if you want to try that out as a method for concentrating the tincture. It's likely to have good keeping properties when kept in a closed bottle and protected from light, and the liquid form can help with measuring the doses once you've established its concentration one way or another.
And I'm super-stoked to find that this tannin removal method has proven to be so useful to you