How come my MOSFET was a "smoking", I thought it was rated high enough.

@OP:
MOSFET specs are funny beasts. In fact, the BUZ71 is a very marginal
device, but the original IRF3205 will probably work for your app if you
wire it up properly, even though not a logic-level device.

All this means is wire S=gnd, D=low side of bulb, and G to the Arduino
pin through a 1K resistor [simply provides a little protection for the
I/O pin]. It would probably also help to wire a 1N400x diode across
the lamp [in reverse polarity] to quench possible turn-off spikes.

Be sure to connect Arduino gnd to MOSFET S-pin.

First off, BUZ17 says 17A, but it's realistically only good for maybe 3-5A
tops. This is because Rds(on) = 0.1 ohm, so Pd = 17170.1 = 30W
approx, when Id=17A. That's FAR FAR too much disspation for a TO220
part, no matter what the spec says. It'll melt, even if heat-sinked.
It might just work for your app, although Pd will still be 2W or so.

Secondly, looking at the spec for the IRF3205, esp Fig 2, even with
Vgs=5V, you should be able to pump 4-5A through the device [see
curve intersection at Vds=0.1V, far left]. Rds(on) is low, so
heat dissipation should not be a big factor.

I'd try it and see what happens. Alternatively, if the IRF3205 doesn't
turn on fully [Vgs > 0.1V], you could try the hookup shown by MarkT,
and use the BUZ71 for the 1st stage and the IRF3205 for the 2nd stage.

Realistically speaking, once Pd gets over maybe 3-5W for a TO220
package, they start to get quite warm, although heatsinking helps.