Since you mentioned that your ONT is 2.5 Gbps, I am assuming that you need a twisted-pair NIC. I don't have a recommendation for a NIC exactly for 2.5 Gbps, but since you're specifically looking for low operating temperature, you may want to avoid 10 Gbps twisted-pair NICs.
10GBaseT -- sometimes called 10G copper, but 10Gbps DACs also use copper -- operates very hot, whether in an SFP+ module or as a NIC. The latter is observable just by looking at the relatively large heat sinks needed for some cards. This is an inevitable result of trying to push 800 MSymbols/sec over pairs of copper wires, and it's lucky to exceed 55 meters on CAT6. It's impressive how far copper wire has come, but the end is nigh.
Now, it could be that when a 10 Gbps NIC is only linked at 2.5 Gbps, it could drop into a lower power state. But my experience with the 10/100/1000 baseT specs suggest that the PHY on a 10 Gbps NIC will just repeat the signals four times, to produce the same transmission of the quarter-as-fast 2.5 Gbps spec. So possibly no heat savings there.
A dedicated 2.5 Gbps card would likely operate cooler and is more likely to be available as a single port, which would fit in your available PCIe ports. Whereas 802.3bz 2.5/5/10 Gbps NICs tend to be dual-port.
A final note: you might find "2.5 Gbps RJ45 SFP+" modules online. But I'm not aware of a formal 802.3 spec that defines the 2.5/5 Gbps speeds for modular connectors, so these modules probably won't work with SFP+ NICs.