Get your new batt, and buy one of these:
Battery Tender Plus - Batterytender.com

On the web, for < $50. Be sure to get the alligator clips: they clip on,
under the hood. Keep it hooked while sitting, or every few days for a
24 hr period.

Besides the AZ heat, the Tender will keep your new batt working for years.
Or, buy the Tender and put it on your current batt:
it will bring it back as far as it can, but the current batt may be near termination.
GL, mD