Disclaimer: This might void your warranty, and if you break something i am not responsible. This was an easy 5 minute job for me, but i'm experienced at ripping apart laptops and phones for things like this.
I really should have taken pics myself, but i thought i'd come share my finding here where the most people would see it.
I've had my DIR-890L for well over a year now and due to the firmware not doing what i expected from a high end router, i've been running DD-WRT since the second week of ownership - and noticed that the temperatures of the router were often quite high - even with low or zero load - sticking to an almost perfect 76C at all times (idle and load)
Today i decided to open the unit up and dust it out, and noticed something odd in this iFixit guide - the one heatsink they removed had no thermal paste or thermal pad under it!
https://www.ifixit.com/Guide/D-Link+DIR-890L+Motherboard++Replacement/72067
So i took to my trusty screwdriver and other than one aerial socket popping loose to remove the shell it was super easy to get into, and i discovered mine was the same as that image - the rightmost heatsink has zero thermal interface material (henceforth called TIM) and the left one had a thermal pad *and* a dried out splotch of thermal paste too.
I did what any good PC techy would do and immediately cleaned them with with 100% pure isopropyl alcohol and squirted a large (compared to PC usage) amount of Arctic Cooling MX-4 thermal paste in there, screwed them back on and re-assembled the unit and saw something new - a temperature under 50C :O
I've left it alone for an hour now in normal use (netflix load thanks to the family) and the temps have stayed heaps lower than before (same ambient temps due to thermostat on the heater, its winter here) and the temps have stayed consistently lower.
http://img.techpowerup.org/170804/capture512.jpg
I get the feeling that as these routers age and with the high usage people stick on such expensive routers, that these heat issues will get worse and worse over time as that thermal paste degrades, causing performance issues, dropouts, crashes and reboots. If you are a brave soul and feel like spending $5 on thermal paste, take some pics for me since i forgot to take my own