Triumph uses overflow bottles that are intended for other bikes. This means the indicated levels can be incorrect, and keeping the level at the low mark seems to keep the bike from peeing out coolant from time to time.
Check your cap. More than a few Triumphs (not just R3's) have had issues with caps that do not have the required spring rates.
Most of the overflow issues are due to post-boiling. This is the coolant boiling in the block and heads after the bike is shut off. The pressure in the cooling system rises and the valve in the cap lifts the spring - letting coolant flow into the overflow bottle. A lot of this can be reduced with better heat transfer from the coolant. Water cools much better than antifreeze, so running more antifreeze than required is not a good thing.
I live in the Deep South where winter temps rarely drop into the high teens *F, it never gets near freezing in my garage, and I don't ride is sub-freezine temps. As a result, I have no need for antifreeze protection to -60*F that is offered by a 50/50 mix. Instead, I use 20-25% propylene glycol (PG) antifreeze with distilled water and a SMALL amount of surfactant. This still protects down to temps into the teens, prevents corrosion, and lubricates seals.
A surfactant is a detergent that reduces the surface tension of water. Using it in coolant allows the coolant to make smaller bubbles when it boils in localized hot spots. Smaller bubbles are easier to carry away and cool the effected area. Products such as Water Wetter, Purple Ice, etc. are commercial surfactants, and despite their lables, very little is required. More than two cap-fulls in most bikes can coat block internals and reduce cooling. 2-3 drops of Soft Soap or any liquid detergent has the same effect. More is not better.
Make sure you ONLY use distilled or deionized water in your bikes!
Tap water has minerals and chlorine in it that will cause electrolytic corrosion in the cooling system in little time. I had a friend that flushed the coolant out of one of his bikes for track day use with tap water. He rode it this way all summer. He forgot (or never got around) to changing it out afterwards, and left it over the winter. The next spring, the bike leaked water the first time he rode it - all caused by corrosion in less than a year. It took milling the head and block deck to fix it.
If you try the above, and still have issues with heat while riding in a pack, or at low speed stop/go riding, Muzzy's sells aluminum radiator fan blades that are easy to install to the stock fan motor, and push considerably more air than the stock fan.
Not everyone will have issues with running warmer than normal, but for those who do, I hope this helps.
