MOSFET-Controlled NTC Bypass

I need a compact RC timing network that drives a MOSFET to short-out an NTC after start-up so the circuit acts as an inrush-current limiter only for the first few hundred milliseconds. The system runs from a 110 V DC bus and the load can draw up to 10 A once the bypass closes... (Budget: $10 - $30 USD, Jobs: Analog Electronics, Circuit Design, Electrical Engineering, Electronic Design, Electronics, PCB Design and Layout, PCB Layout, Simulation)