No they won't. Trust me, you need to turn your heaters on. Heat is a critical element to solvent printing, without it it does not work right. Solvent inks require heat to form a bond with the media. The only way you can get away with running less heat is if you're running a true full solvent printer like a Vutek, but even then heat is required. On anything short of that, be it Roland, Mimaki, Mutoh, Seiko, HP or whatever, no heat means no ink bond.
If you're not running heat because the media is tunneling or buckling under it, that's a sign you need to either adjust the heat down, adjust the tension on the takeup reel, or use higher quality material. You said 13oz so I assume this is a 13oz super-smooth scrimless material (god I hope these banners aren't going outside if it is), that stuff can't take a ton of heat but it still needs some.