Excellent! My apologies, as usual I did not note who the poster was

and more often than not I see so many car projects like this that are so misguided or false. [Anyone for fuel polarisers; or mobile phone chargers to improve EMS & performance; or resistors - maybe even their
hi-tech voltage-regulator version - to trick EMSs into
better performance LOL (which would blow engines if they actually worked for leaner mixtures!)...?

]
But cool - you said it - engine soak. And as I recall some of those Italians could suffer badly.
Incidentally, I suppose you have the normal crank driven water pump... you haven't removed the engine's (mechanical) thermostat and fitted an electric system?
If the Hella is a direct plugin for the fan relay (with added small terminal wiring) then I'd be tempted. My only concern would be if it draws current with IGN off - ie, from what I've seen such relays tend to use 555 timers and they have their 10mA standby draw. That's no problem for their fuel pump control relays (missing pulse aka tachometric 555 circuits) because they are powered via IGN +12V, but not seeing in the above relay schematic what timing circuit is used nor how it is powered after IGN off...
But I haven't examined your detail. I'd even have to look up whether 15 & 31 are IGN etc!
However I'd be tempted to use a DEI 528T or similar. That too has its 555 10mA drain but it should be easy having it power itself off tho that might require an extra relay (and 528T) if you want the fan to come on if
whatever temp sensor hits your desired fan-on threshold within
x-minutes of engine/IGN turn off.
My main attraction for the 528T is the use of available parts etc and the NON-use of specialised relays. (I prefer standard (SPDT) relays with external controls, even external quenching diodes etc.)
FYI - I'm looking at a similar 528T set up for
bach939 in
adding additional accessory to door locking. That's to use 528Ts but I need to check 555 (& 528T) trigger behavior wrt to power-on timing, etc.
Are you after stealth? IE - are you seeking originality in looks etc?
My solution to that was the use of a PICAXE 08 (08M2) which are 8-pin devices the same size as a 555 timer but without the need for larger timing capacitors etc. Excluding their output MOSFETs etc they could even be concealed within wiring - and reprogrammed without removal or direct access (run their programming input wire to somewhere suitable).
And the 08M2's standby current is far less than leakage current of automotive batteries so even fulltime powering is not an issue.
That does require the usual circuit construction ability (soldering etc) plus a serial interface & PC or maybe smartphone etc for programming plus the associated learning curve. However the latter is greatly simplified by the plethora of existing web projects (ie - copy & paste code) and once established is far easier than working with traditional circuitry... there is no need to overcome tricky electronic designs nor change or adjust componentry; just reprogram the new function or change parameters.
One
standard 08M2 PCB or circuit can handle so many functions - ie include onboard LM7805 voltahe regulator (TO-92 package); 2 programming resistors; one MOSFET output; other inputs & outputs with provision for a series & pull up or down resistors & filter cap etc and a MOSFET for outputs.
IMO the 08M2 is perfect. It can be an add-on that uses the existing fan relay (probably without diodes if ground-switched sensors/controllers are used) and overcomes all problems... EG - switch or keep the fan on if whatever sensors are above a certain temp even with IGN off unless IGN has not been on for 5 minutes, and do not run for more than 3 minutes or if battery voltage is less than 12.4V... and BTW - flash that dash warning if the battery voltage is less than 13.4V with engine running else 12.6V & quicker if it's less than 12.4V (or get my battery monitoring program to text the dash's alphanumneric display next time the IGN key is inserted or turned on..).
That's merely a bit of brainstorming in case you are interested.
Otherwise it's back to traditional
physical circuit implementations. And that's pending for me (I'm avoiding circuit DIYs like 555s & 08M2s for
bach939).