MOSFET getting hot. Is it normal?
Yes, it is expected that running this MOSFET without a heatsink will get surprisingly hot even with very little power dissipation. Note this section of the datasheet:

notes are on page 9:

Dissipating 3W with a &quot;typical&quot; heatsink would give a typical temperature rise of \$  ( R_{\theta JC}\text{ of }1.11\text{}\frac{^{o}C}{Watt}  + R_{\theta CS}\text{ of }0.5\text{}\frac{^{o}C}{Watt} + R_{\theta SA}\text{heatsink to ambient} ) \times 3\text{}W = \text{approx }5^{o}C \$
Typical numbers are not guaranteed, but are a good general guideline. They didn't specify the heatsink but just any &quot;flat greased surface&quot;.
However, dissipating 3W without any heatsink would give a Junction-to-Ambient temperature rise of \$  R_{\theta JA}\text{ of }62\text{}\frac{^{o}C}{Watt} \times 3\text{}W = 180^{o}C\$ (maximum). It might not get that high, but it will certainly get very hot. The Junction-to-Ambient thermal resistance is extremely high.
Unlike the typical &quot;Case-to-Sink, Flat Greased Surface&quot;, the Junction-to-Ambient maximum rating does actually spell out the physical mounting in note 5: one square inch of printed circuit board (25.4mm x 25.4mm), and they do mean for most of that to be copper (which provides some amount of heat sink). This is a pretty good approximation of the heat sinking that happens in a circuit when there isn't a &quot;heat sink&quot; attached to the FET, instead the heat finds its way out of the very-hot junction by thermal conduction through the leads of the device, into the less-hot parts of the circuit. So there is some natural heat sinking that occurs, but at a very high thermal resistance, so it does get very hot with very little power dissipation.
Heatsinking is very important for FET, because unlike a BJT, FETs are subject to a harmful effect called thermal runaway: when a FET starts to overheat due to excessive drain current, its threshold voltage decreases -- which effectively drives the FET even harder, making it heat up more, making its threshold voltage decrease even more... Usually we either guard against the problem by overdesigning the heat sink to stay well away from thermal runaway.