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Incubation chamber

Hello,
I'm working on a project involving 160 w, 230 V, 8,5 m long heating cable wound on a copper chassis. The heating element heats approx. 2 cubic meters of air inside an insulated rack. I'd like to put the chassis on the floor of this rack and measure temp somewhere near the middle of it.
The question is if there is any simple way to control the amount of the current ("heat"?) flowing through the heating element. Maybe I am overthinking this, but I saw a solution with SSR and using extra low frequency PWM pulses controlled by PID and it just doesn't seem right to me.
I want to achieve direct control of the current flowing through this cable with an ambient temperature sensor - If the settemp is almost reached, it lowers the current, and vice versa. I suppose that mosfet could do the job instead? Or should I switch the current manually to get the fine tuning done (So it doesn't switch too often) and let the PID handle the SSR like a bang-bang.
I still struggle to understand few...

Incubation chamber

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