Obtaining varying voltage from a constant voltage power supply
Use a PWM generating chip like the LTC6992 and drive an N channel MOSFET (a type with low on resistance) on and off from the output (or via a driver chip). The MOSFET source can be grounded to make life easy and, the nichrome wire can connect between drain and 24V supply.

The fact that you are hitting the nichrome wire with high frequency PWM should not be a problem if you are just using it to heat something up.

LTC6992: -



If your wire is long (i.e. has significant inductance) then it's prudent to use a flyback diode to protect the MOSFET from back-emf flybacks.

MOSFET: -



Replace the lamp with the nichrome wire. +Vin is from the PWM generator which can also be a 55 timer circuit.