Several potential issues here.
 Are the relays getting hot because of heat from the relay coils or because of high resistance of the contacts or inadequate ventilation ?
 Your relays should be warm not hot especially not too hot to touch. Relays can degrade with 'shorted turns' in its coil, the effect of this is that the relay will still operate but will draw more current and get hotter creating more shorted turns and more heat eventually failing but with the potential of catching fire, burning out wiring/switching components or if lucky just blowing a fuse.
My initial response would be a visit to my local auto elec with a view to getting better quality relays, ie higher resistance windings for less heat dissipation and correctly/over rated contacts.
Oils aint oils. There's definitely 3 different 'levels' of auto relays, cheap Chinese junk, consumer, and quality. You're only after 2 so financially not a big deal to get the quality ones.
I had an issue several years ago with my ARB twin motor compressor which is a well engineered and built machine but was let down with the cheap Chinese relays fitted. They rattled themselves to pieces on the 'Highway' between Taralinga Well and Emu. I replaced them with quality, at the time $20, relays and haven't had a failure since (4 years).
A trick if the issue is that the relay is running at or close to maximum current is to replace it with a 'driving light' type relay which has two sets of contacts (one for each light) and common these to halve the current through each contact.
Deano 

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