I'd say you may not have the best part right there.
Go Digikey, search "mosfet", select "SO-8, 8-SOIC, 8-SOP".
Or look at this page:
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Handling 10 amps is no sweat with most of these.
You can get SO-8 fets with an rDSon of only a few milliohms, and they're way simpler to mount. Don't even need to drill a hole. You'd think a SO-8 wouldn't be able to handle power due to the smaller leads alone, but you parallel 3 leads on one side and 4 on the other which gives a LOT of current ability. They have a very low junction-to-lead thermal impedance so a wide trace can dissipate a surprising amount of heat!
And look at switching losses. The IRF3703 is a very large gate charge. Don't underestimate the energy lost in charging and discharging that capacitance. And higher capacitances mean lower rise and fall times for a given driver, which can increase switching losses.
I have a bunch of IRF7811W SO-8 that I use, 0.009 mOhm rDSon, 14 amps continuous with no heat sink, and the gate charge is 18. And I use them because they're cheap. $0.86/ea in small quantities. Gate charge on the IRF3703 is 209. So it's more that 11 times slower to switch on the same driver, and even if your driver is big then you're still spending 11x more total energy to charge that cap per cycle.
Due to cost, size, and mounting issues, if I needed to switch 20 amps I'd greatly prefer 2, 4, whatever of these over a TO-220 or anything with a heatsink. Smaller, easier, and cheaper especially if the TO-220 would need a heatsink.