Greetings Thomas,
With regards to your carburettor you might like to take a look at a post I put up some time ago back,http://www.trf.org.uk/forum/viewtopic.php?f=84&t=18173&start=20&hilit=carburettor
Fit new seals and gaskets and inspect the air intake hose to air filter box for security and possible splits. The air filter can be washed in a degreaser fluid such as Jizer, wash with warm soapy water, air dry or with compressed air and then the filter coated with K&N aerosol spray.
Really, wether it needs it or not, I would suggest that you carry out a full service of the fuel system, plus the whole bike so that you familiarise yourself with where all the various parts are situated. Trust me it gives confidence and saves time if you were unlikely to have problems en route.
The carburettor is easy enough to remove and to work on, with obvious caveats about cleanliness and 'sharp' screwdrivers. I cleaned mine in a sonic bath which I bought from Aldi and cleaner fluid from Maplin.
The fuel tap has a filter but I replaced the complete tap which has a Reserve position, far more useful than a warning light in my view. I got the tap from Steve Goode as a direct replacement, good service too.
I replaced the original spark plug, kept as a spare, and replaced it with an NGK Iridium, costs a little more but last longer and operate under harsher conditions.
The handlebar switch gear I stripped, cleaned with aerosol brake & clutch cleaner, sprayed it all with aerosol lube plus coated it all with silicon grease, available from a plumbers merchant. The switches are quite clunky and the spring loaded balls have a tendency to stick.
Disconnect all the electrical contacts that you can find, thoroughly clean them with B&C cleaner, silicon and fit them together securely, any doubt use a backup tie cable. Thoroughly recharge the battery, preferably with one of the new type of chargers - I use an Optimate 6 which is worth every penny. The battery is fitted permanently with an extra charging lead, which I connect after every ride.
Remember that an additional oil filter is fitted just below the headstock, the frame has an extra drain screw on the right above the carburettor, try to drain when their is warm/hot so that it flows out easier. The system is 'dry sump' and so you can only check the oil level after the engine has been running for about 10 minutes. Drain it all, replace the paper filter and its seals (I used genuine Suzuki items) and replenish with 2 litres of new oil, run the engine and then recheck the dip stick.
In my opinion the engine does run 'hot' in comparison to other bikes but it is an air cooled unit which relies also on plenty of oil flow, hence the need to use clean oil. I use semi synthetic Rock motorcycle oil, never use car oil. The inside of my right calf feels the heat as the exhaust runs close to the frame.
If you still have problems then come back to us and we will try to guide you further.
TTFN
Hugh.
Ps forgot to mention that I extended the breather to run up under the tank, before looping back to just above the engine, I left the overflow pipe as original so that if the carb flooded it would drain safely. The breather pipe has to be kept away from possible water ingress and I have been through some really deep water with this bike. The fuel filler cap is a naff design and will allow water in to the tank if you remove the filler after a day running in the rain,
, so periodically drain the tank thoroughly by removing the tap completely.