"...............sudden cooling issues ................"
A "sudden" rise in temperature is usually caused by rapid loss of coolant, restriction of air or coolant flow.
Check for:
# Collapsing coolant hose.
# Loose component in engine compartment, intermittently restricting air flow in/out of cowling.
# Correctly functioning radiator cap.
# Temperature gauge or sender/sensor malfunction.
"After the CHT temp rose to 260F I shut the engine down."
I am intrigued - how did you continue the flight?
In general you should not "shut down" a hot engine - you should keep the engine running at reduced power to maintain coolant/oil flow and enter a shallow descent, to maintain good air flow - land at the earliest opportunity to assess problem.
".......overflow bottle had very little coolant in it after fluid had gotten this hot."
The overflow bottle is actually an expansion tank ie it allows for heated/expanding coolant to escape and on cooling, return to the cooling system. The fluid level should be part of your preflight checks. The cool fluid level, should be around 1/3 to 1/2 of the expansion tank - the level will rise when engine hot. There should be very little discernible change in the fluid level between service activity. Any change, from the usual level, should be cause for concern.
Note: fluid level, in the cooling system (under radiator cap) should be completely full at all times (no air gap).
127C (260F) is a high temperature but within Rotax maximum limits - this alone would not cause your expansion tank to empty ie there must be another factor.
The "water" pump is, at best, a marginal performer - its job is to maintain a posative flow in one direction. If its connected & rotating with engine turn over it is likely to be working as designed ie nothing wrong.
I would start by checking your temperature monitoring system - it may be giving false readings.
At the same time - check the radiator cap is in good condition & meets the current Rotax part number.
I assume you have replaced all rubber components at the Rotax recommended 5 year interval. This is also an opportunity to replace the coolant (Personally I do this at 2.5 years). Use quality concernatre at 50:50 mix with pure (not tap) water.
