Does the Lambda relay always get hot?

[Bitsyncmaster]

No. The heat is caused by the coil current in that relay. The standard relays use less current. I will look if I still have the OEM lambda relay and measure it.

Edit:
I found the OEM lambda relay. Tested and not as bad as I thought. I guess the smaller case makes it get hotter.
61 ohms = 221 ma at 13.5 volts = 2.98 watts

Standard relay
86 ohms = 157 ma at 13.5 volts = 2.11 watts

Just finished painting the first 10 lambda relays. I tested with a 4 amp load (I tested lambda current a bout 2 amps) so power (heat produced) is 0.10 watts. So basically my lambda relay will run at ambient temperature. This is plug and play but only to be used for the lambda relay socket (yellow socket). I'm pricing the lambda relay at $69 shipped to US locations.

Now the relays always on, RPM, lambda and AUX relays are the ones producing the most heat in the relay compartment. I run my standard solid state relays for the AUX relays but they do no have the large power and ground pins.