RJ-50 Captain reported Electronic Flight Instrument System cooling warnings and subsequent loss of both Primary Flight Displays in climb and later in cruise. Crew continued to destination in accordance with checklist guidance and landed normally.

Narrative

Dual MFD (Multi-Function Display) failureWhile climbing on departure from ZZZ1; DISPLAY COOL caution message showed on EICAS. FO was Pilot Flying and CA was Pilot Monitoring. I announced Display cool caution msg and FO called for QRC; QRH for DISPLAY COOL msg. I referenced and went through DISPLAY COOL QRH and do the procedure; msg went away and did not occurred in the next 45 minutes. While on cruise MFD 1 failed and as FO was already PF; I decided to keep it that way and run MFD FAILURE checklist and was not able to reset the MFD; in that moment ATC indicated to fly direct ZZZZZ fix a few moments later ATC asked if we were flying to the fix as we were flying on a heading around some weather. I advised we were troubleshooting our display screens and we might need advise from them to see if we were flying to the fix; they responded yes moments later. After we were flying to ZZZZZ MFD2 failed and once again run MFD fail checklist without a successful reset. Then few minutes later DISPLAY COOL showed again and run respective checklist again this time msg did not extinguished after 60 Seconds. Checklist mentioned land at nearest suitable airport and a note mentioning All displays will keep functioning for at least 30 minutes after fan failure I decided to take control of aircraft and [request priority handling] as we will need assist with navigation as we could lost all screens in the airplane. I asked FO to advise Flight Attendants and not to do a PA as I discussed with FO about two MFD failure as at that moment was not necessary for a PA; in case we would lost full screens we would make an announcement; we sent ACARS messages to Maintenance and Dispatch about situation and advised we might need to divert and as we were on the descent to ZZZ we decided to continue and Dispatch also agreed with continuing to destination. ATC was helpful providing vectors to ZZZ and flew a normal to RWY XXR ILS to a normal and stable landing taxied to gate with no more incidents and called Maintenance; Dispatch and Chief Pilot upon reaching gate.'