1k resistor. provides about 10ma to Light Emitting Diode. Voltage drop across diode is around 1.8v.
(12v-1.8v)
----------------------------------------- =resistance
(current rating in amps)
in this case safe setting is assuming 10ma, or 0.01A, =1k resistance
as for the bed itself it is 1-2ohms
and for voltage drop across thermistor it is 4.7k.