Can hydraulic brake levers get hot when brakes overheat? If your hydraulic brakes get hot, can this heat ever travel to your brake levers. Can your levers feel hot or is this my imagination?
No, the thermal conductivity of brake hose/fluid is way too low.

I've run the numbers on this -- very roughly to make the calculations simpler.  I've assumed the hose isn't cooled by airflow for some reason and a solid hose or equivalently that the fluid has the same thermal conductivity.  Even the lever is assumed not to lose any heat to the air.  All these assumptions maximise the amount of heat delivered to the lever.

Lets assume the hose is PTFE, which decomposes above about 200&deg;C and has a thermal conductivity of 0.5&nbsp;W/m.K (the highest value I saw).  I'll take a hose outside diameter of 6&nbsp;mm, length 1&nbsp;m.  To feel warm the lever would have to get to something like 40&deg;C, giving a temperature drop of 160&deg;C at the point where the caliper end of the hose got so it it would be giving off toxic fumes, i.e. the absolute maximum.  

Working this through, you'd be conducting 2&nbsp;mW of heat to the lever.  If the lever is 100&nbsp;g of aluminium with a specific heat capacity of 900&nbsp;J/kgK, this 2&nbsp;mW it would take 12.5 hours to warm by 1&deg;C.

Some steels have 100&times; the thermal conductivity of PTFE.  Brake cables could conduct 200&nbsp;mW for the same caliper temperature, and only take 7.5 minutes to warm by 1&deg;C - but still an hour or two of non-stop braking to get from ambient to warm.