I'm so sorry for your loss.
That open sore was probably columnaris. It's also responsible for the fin rot. It's a bacterial infection, quite common in the summer as it just loves warm water. Apparently it lives in the water all the time, but is opportunistic in infecting sick, stressed, injured, elderly or otherwise immune compromised fish. Bettas are really susceptible to it and even the best-kept tanks can suffer a bout of 'fungus' -- it sometimes causes fuzzy patches, but not always, sometimes it's internal and manifests as organ damage or septicemia, causes open sores or infests the gills with no outward signs or 'fuzziness'.
Raising the heat is not always good - this infection loves heat and it speeds up..
Clean your bowl with a non-detergent bleach solution and leave it the sun a few days after rinsing it well, if you wish to get another betta for it.
Better, throw the 1 gallon bowl away and get a bigger tank, or make sure you change the water more frequently to avoid ammonia build-up, which can lead to weaker slime coat, gill problems and other issues, including weak immune responses to this disease.
Last edited by Aus; 06-17-2012 at 03:04 PM.