You need to get a fan if you can quick. Without a fan, snowmobile
Engine heat tends to run away. When my fan stoped working on one of my Rotax swap it hit 220F really quick. Americanvolt.com has thermo switches for any of your plans. 12" standard fan from eBay is like $25 and they work fine.
For your gearbox, make sure you over-fill with good oil. Over-fill it right to the top. About 2-qt. This will insure your nice new expensive input shaft and needle bearings are resting in oil, and getting the much needed lubrication at all times. I over-fill mine until the oil comes out of the fill plug! I use RedLine Shockproof Gear oil. Either the heavy-weight or light-weight are both very good protective oils for gears and bearings.