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Lyot Crater may be the result of a relatively recent cometary impact on the Martian surface. There is no sign of extensive warming because of it, however.

Observe the crater here in an MOC Atlas image <a
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The crater is very shallow, though very large. There is an extraordinary ray system -- a sign of the crater's relative youth. The central area of the crater is very hummocky, and close ups here and for many diameters from the crater show what look a lot like lakes among the hills.

The impact was in the northern lowlands, in an area widely assumed to be a remnant sea bed. While there may have been some liquefaction of a frozen surface due to the heat of impact, the overall impression of the crater and its region of influence is remarkably dry. For example, there are very few (and mostly very tiny) channels associated with the crater and its debris.
Liquid water may well have been released, but if so, it was in very limited amounts.

What is noticeable is the extensive disruption and foundering of the Arabian "shore" just south of the crater. These "mensae" are found all along the Arabian margin, but here they are particularly apparent, and close ups show many areas of chaotic terrain within the mensae and within craters in Arabia as well. It appears that the impact caused immense disruption --
through intense shaking among other things -- throughout the region, but it did not, so far as can be seen, cause significant channeling, release of water, or signs of significant surface or atmospheric heating.

This is actually a surprising result if one expects a cometary impact to significantly increase atmospheric density leading to a greenhouse effect sufficient to release water and lead to an eventually clement Martian surface. It's possible there was an increase in atmospheric density following the Lyot event, but only a limited, maybe even an absent greenhouse effect.

Here's a paper to consider: http://www.lpi.usra.edu/meetings/lpsc2002/pdf/1688.pdf

Is it possible, instead, that Mars is simply too cold and has pretty much always been too cold for external impact events to significantly affect its climate for extended periods?

In other words, is it possible that the only way to warm the surface of Mars sufficiently to increase atmospheric density and release substantial quantities of water is through release of internal heat, that no impact would do the trick?

In that regard, it is worth noticing that vast areas of the Martian surface appear to have been flooded with lava or subjected to intense volcanism (both on the Highlands and Lowlands) relatively recently. Clearly release of internal heat has been vitally
important in Mars' past.

As for aiming comets at planets to see what happens when they crash... let's not.

Cheers, BFelix