This is simply not true. Look at the two example files I attached. It's exacly the same scenario except that the first one is as flat as a snooker table, the second one has got hills, lots of burning tiles, etc.
The times on my PC:
version 1: AI planning time 3sec, Blue bar time 6sec
version 2: AI planning time 3sec, Blue bar time <2sec
And this is not surprising, because in the flat example, many more lines of sight exist between units, so there have to be many more calculations which unit will attack which one with which weapon (In this case no one attacks because I picked units which can't harm each other at that distance.
Naturally, burning tiles can increase the blue bar time, but only due to their effect on the action in the turn, e.g. calculations whether the adjacent tiles start burning as well, pathfinding, etc ... but the effect is minimal compared to those calculations related to the number of units and most importantly, it doesn't have to do with the graphics of the burning tiles. timetest-scenarios.zip