Diode Temperature effect
The forward voltage of a Si diode will drop by about 2.1 mV/°C (negative temperature coefficient, NTC). For a Ge diode this NTC is a bit higher at 2.5 mV/°C.
The effect is almost perfectly linear, so if you want you can make the diode a temperature sensor by supplying it with a constant current.  

Reverse current increases exponentially with rising temperature. For a 1N4148 it increases tenfold for every 20°C temperature rise.