Your going to need to pick up a heater unless you keep your house at 86*F. I would suggest getting a 25watt adjustable heater so you can set it to the temperature you need. Most preset heaters will not get high enough.
If the heater is too big to fit in your tank you can get a cheap plastic bin from the dollar store or wal-mart and use it as you "hospital tank". Heat it to 86*F and keep it really dark (maybe keep a towel over it). Change the water every day with fresh (dechlorinated) water. Clean water will help perk him up and it will remove the velvet from the tank as it dies.
Start doing 100% changes every single day. I think the reason your fish got velvet is because he wasn't getting enough water changes. A 1 gallon should get 3-4 water changes a week (roughly every other day).
If you get the medication (or any medication for that matter) your going to want to turn your filter off and take out the carbon cartridge. I'm not exactly sure why but all the medications recommend doing this.
Hopefully Adastra or OFL will chime in. I've only dealt with Velvet once but I had success with this method.