Hi,
Although , the recommended RAM for the ASA 8.3+ is 2 GB , I understand that this vulnerability require upgrade to ASA 8.4 + to resolve this.
http://www.cisco.com/c/en/us/products/collateral/security/asa-5500-series-next-generation-firewalls/product_bulletin_c25-586414.html
For this reason , i would recommend an upgrade to the ASA 8.4.7.23 to fix this issue.
You can also monitor the memory utilization on the ASA device after the upgrade. If it is stable , you can plan an upgrade to ASA 9.x code in future.
You would have to contact Cisco TAC to get this interim version.
Thanks and Regards,
Vibhor Amrodia