Random SFP negotiate question

Can't find a google solution to the actual issue we're having:

We have remote office space in a very large building (not ours), where the ISP demarks about 1100 feet from our network closet. There are no network hops between the demark and our equipment. We ran single mode fiber between the demark and our office space, but the ISP terminates in copper (its a small speed circuit). We are using fiber/copper converters on both ends. It has been working for about 6 months, until last week it suddenly stopped. Upon review, when it was setup, the only SFPs available were SM 10gb SFP+ with 10km distances. When I touched the demark SFP, it was so hot I couldn't hang on to it.
So my colleagues and I are debating....will the 10gb SFP+ "negotiate" to what it needs to, or do we need less power (2km distance)? All we have on hand are the 10GBSFP+ modules, we have no 1 gb SFPs on hand. Some people want to go ahead and use the 10gb modules, thinking the 2km vs 10km power difference will keep it from overheating. I'm not disagreeing, but I am skeptical that the little fiber/copper converter boxes will do the right thing when presented with a 10gb SFP+, and I don't want to burn up anything.

So, Reddit, what say you? In this situation, what is the potential fallout from using the 10gb modules to go from Circuit-copper-converter-SFP-SM fiber-SFP-converter-copper-switch?