Welcome to the forum
I`m very sorry to hear about your Betta, it`s sad when that happens and it can be very difficult understanding why it does happen.
I`m relatively new to looking after Bettas but now have 3 after realising what great fish they are.
When I got my first Betta he went into the 37G tank with a few of the other community fish I have so I too was a bit unsure about letting the water `sit`.
I set my 13G up with the water conditioner, decorations, plants, heater and filter etc and left it for about 1-1 and a half hours to allow the water to get to approx temp required for a Betta. You may find that your Betta will hide and appear to be a bit depressed within the first couple of days and also that he may not seem to be interested in food at all. It`s easy for me to say now but please don`t worry if you do experience this as it`s quite common and your new fella will settle and get used to his surroundings.
Hope all goes well with your next Betta, don`t hesitate to come back and let us know how you`re getting on?