My main Dreamcast has the gdemu v5.15b & stock PSU running warm too and it holds time & date fine. However, I also have 3 others with no gdemu and they too all have the same battery mod as you. When I boot up my others, I usually have to input the time & date again on my spares, because I only test them every month or so. However, I was told that this is odd behavior and that it should just be perfect for several months, I have a friend whose time & date kept after like 90 days, and by comparison, mine will not.
However, they seem to hold enough juice for several weeks and recharge upon booting up. Idk if anyone else has experienced this, PSU issue or what?
And NightBreeze is correct, you have the right battery.