Depending on how handy you are around electricity, you can attempt a fix. If only one light is firing & you have only 1 ballast, it is likely a connection problem, may be corrosion of a connection. I don't think heat is the problem - for one thing heat will fry the ballast & both lights would be out. <Unless there is actually 2 ballasts inside. BTW - the new lights use electronic ballasts so would not have starters at all.> More likely, it is moisture buildup under the canopy that caused problems.
First, make sure that the end cap (the bulb plugs in thing) is not corroded or loose. Also, if you have individual switches for each light, make sure those are not corroded open. Next, I would take the thing apart & seeing if there is anything obvious. If the wiring & both endcaps are fine (maybe swap the good endcap to the bad side & see if that work), then you can try swaping out the ballast <depending on the condition of the light, that might or might not be economical.>
Disclaimer: Working with electrical stuff requires some experience & a good dose of common sense .... Proceed at your own risk!!
80 gal FW with 30 gal DIY wet/dry/sump.
9 fancy golds, 1 hillstream loaches, 1 rubber-lip pleco (C. thomasi), 3 SAEs, small school of white cloud minnows, planted.