I could not find any research-based recommendations for children of this age group.
But I can answer a part of your question. At least one source is not consistent with your hypothesis that the ideal bath temperature would decrease as the baby grows. For a broad age group (including adults and not restricted to children) it is actually higher (40-42.5°C, see Haghayegh et al, 2019) than the one you list for babies (36-38°C). This study was limited to the effects of warm/hot bath/shower on sleep. What this means is that at some point in life, we can tolerate much higher bedtime bath/shower temperature, and it may even be optimal for sleep. This study does not mean that such relatively high temperature is recommended for 10-month-old infants.
Additionally, The Royal Children's Hospital recommends 37-38°C for "a child's bath", not specifying the age range. It further specifies that it should be "comfortably warm" to touch. No scientific research is cited, though.
Water-based passive body heating (PBHWB) as a warm shower or bath
before bedtime is often recommended as a simple means of improving
sleep. ... PBHWB of 40–42.5 °C was associated with both improved
self-rated sleep quality and [sleep efficiency], and when scheduled
1–2 h before bedtime for little as 10 min significant shortening of
[sleep onset latency].
Haghayegh S, Khoshnevis S, Smolensky MH, Diller KR, Castriotta RJ. Before-bedtime passive body heating by warm shower or bath to improve sleep: A systematic review and meta-analysis. Sleep Med Rev. 2019;46:124-135. doi:10.1016/j.smrv.2019.04.008: https://www.sciencedirect.com/science/article/abs/pii/S1087079218301552
Bath time safety
Young children have very sensitive skin, which means that hot water
can scald them very quickly. A safe temperature for a child’s bath is
between 37°C and 38°C (or about 36°C for a newborn).
Check the water temperature with your wrist or elbow – it should be
comfortably warm, not hot. You might even want to get a water
The Royal Children's Hospital Community Information in consultation with Life Saving Victoria. Melbourne, Australia. Reviewed October 2018: https://www.rch.org.au/kidsinfo/fact_sheets/Safety_Bath_time/#preventing-burns-and-scalds