IRLZ44 - Leads too small for high current?

I have to control a resistive load at very high current (30 amp continuous - won't be much higher than that). I have read that the IRLZ44N is a good MOSFET to use to drive this as it has continuous 100C current of 33 amps and continuous 25C current of 47 amps. Since my power supply is set at 10V, it seems plenty beefy enough for what I need.

But when I got the transistors in the mail, I was shocked to find how small the leads are. They're small enough to jam into a breadboard! It seems to me that the leads will be a huge bottleneck for sourcing so much current and when I hooked up the transistor I convinced myself I was right because the drain and source leads started heating up (I was monitoring the temperature) and then the MOSFET casing cracked.

Here's a few pictures of my setup:

Connector I am using. MOSFET slides in top, screw terminals for wires.

MOSFET connected to heat sink.

Heatsink view.

How do people usually deal with this? Is there some kind of special connector I need?

P-Worm

Better review RDS_on to VGS to ID.
Leads should be short as possible.
Your heatsink is leaving a lot of the body "unsinked", often overlooked is a sparing amount (a dab, not so much that it squishes out from between) of thermate (a/k/a silicon paste, heatsink compound.)
HEXFETs can be configured in parallel - and thereby divide/share the current and beat the reaper.

Was it made by International Rectifier? Or was it a knockoff? I have never had lead heating problems on either IRF-Z44 or IRF-Z48, the latter is rated at 75A continuous and have used plenty in RC aircraft brushed speed controllers.

To expand on runaway_pancake's reply, the Rds(on) for the IRLZ44 is quoted at 0.025 ohms at 25A and Vgs=5v. It may be higher at 30A. Even if it isn't, the power dissipation would be 22.5W which IMO calls for better heatsinking than in your picture. Consider using two of these mosfets in parallel, then they will both be running at around 15A each and will dissipate around 5.5w each, making it much easier to provide adequate heatsinking. Also bear in mind that the tab of the mosfet is connected to the drain lead.

Putting them in parallel sounds like an excellent idea. Thank you for your help.

P-Worm

If it is rated at 33 Amps and you want to run it at 30 Amps then I would use another device or connect two in parallel.