triac - How do I get proportional 240V AC output from an Arduino-based PID controller to "dim" a rice cooker for a Sous-Vide project?

I'm making a PID controller for Sous-Vide, using an Arduino.

I'm trying to decide how to control the output. Using an SSR as an on-off switch on 240V AC will probably give me the result I'm looking for. However, I'd rather have a more continuous proportional output, so the rice cooker can be effectively "dimmed" rather than switched on and off.

What do I need to do this? Is a TRIAC essential? Will certain SSRs do this? Will all SSRs be capable of this? Do I need to build a 240V circuit from components myself, or are such devices available at similar costs to an SSR?

CLARIFICATION

I may have mislead with the word "proportional". I am building a PID with an Arduino. I will use it to drive a dumb rice cooker, and I'll have a temperature probe to detect temperature. This is the background to the question I'm asking.

I think it will be fairly easy to use a relay or SSR to turn the heater on or off every few seconds to control the heat appropriately. However, what I want is to be able to control the heating element so it runs at a fraction of full power, rather than turning on and off all the time. I would prefer this as it gives better temperature control, and I just prefer the idea of a constant electrical load as against switching 2000W or so every few seconds.

So I have a 5V digital output that I can control with a microcontroller (I believe I can control it far faster than 50Hz). I want to use this output to control the heat output of a heating element. I think the right device to use is a 240V SSR. My problem is deciding what sort of SSR I need, and then how to use it. I'd prefer a complete device with power plugs (like a powerswitch tail - http://www.powerswitchtail.com/ - but for 240V, and with the ability to dim rather than just switch on and off).

Answer

Based on the guidance given in other answers, and a realisation that I was trying to do something too complex for my real needs, I decided to order a PowerSwitch Tail IIU 240V. It's a simple relay in a plastic box with power cables attached. It won't solve my "dimming" problem, but as a number of people pointed out, turning on and off every few seconds will likely provide me all the control I really need.

In actual fact, this doesn't answer the original question I asked, but does solve the underlying problem I had. For 110v applications, there is a ZeroCross Tail which would actually do exactly what I wanted, and I'm sure I could adapt such a device to 10A/240V with UK plugs, but for now, I'll settle with the IIU version.