Does it have to be mechanical? Wouldn't an electronic one do the job?
If so perhaps try using a 555 timer. If you need it to control power then simplest way of switching is to use a relay (remember to use a diode to handle the inductive kick of the relay's coil).
http://en.wikipedia.org/wiki/555_timer_IC#Monostable_mode
Now the time delay part is dealt with you need to sort out how to make the switch close after the time delay, rather than turn off after the time delay which is the "default" for a monostable. Relays can be obtained in Normally closed, or normally open, or even in SPDT variants (which would give you a choice depending on which connections where wired up). In addition unlike many ICs the 555 can both source or sink current. This means you can either use the 555 as a source of power for a relay, OR treat it as much like a switch to allow power through a relay. Sourcing and sinking are inverses of each other, so could be used to invert the power verse times output of the 555. Instead of wiring a 555 between the 555 and ground, simply wire the relay between power and the 555. When the 555 is "on" it'll keep the voltage across the relay as 0V so no current will flow. If it's a NO relay that means the relay will be open. When the 555 is "off" the voltage at it's output pin will be 0, so creating a PD across the relay, causing a current flow and closing the NO relay.
Sure maplin did a kit that powers a relay using a 555 monostable. Think it's got a SPDT relay, so you'll have the choice of power off for a time, or power on for a time. If the time ranges aren't suitable, just substitute different values of resistors, and or capacitors, until the circuit's time constant is correct.
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Is it important to see how long the clock has been going?
If so 555 astable generating clock pulses every second. driving a counter which "locks out" the signal from the pulse generator after 3*60=180 pulses. (This is also the "count achieved" signal that would be used to control the relay) Simply reset the counter to start the count. Shouldn't be too difficult to take the count and convert it to lines/values suitable for display on 7 segment LED displays.
If you want time remaining to displayed perhaps use a "count down on pulse" counter, and instead of using the reset functionality, start it by loading with a count of 180, and halt the decrementing pulses when the count reaches 0.