As John Tullamarine has alluded to Vmca is directly proportional to engine thrust.
Think of it in this way... in very cold conditions an engine (jet or piston engine) will produce its maximum (red-line) power. In very hot conditions it will produce considerably less power. Therefore, the power output of the "live" engine is dependant upon the ambient temperature.
Considder the following examples for both hot and cold scenarios:
Cold ambient.
With, for example, your left engine failed, the remaining "live" engine will still produce its red-line maximum thrust. This will produce a yaw towards the "dead" engine. Associated with that yaw there will be a minimum speed for maintaining directional control of the aeroplane by the use of rudder. This is termed Vmca; minimum control speed in the air.
Hot ambient.
With the left engine failed, the remaining "live" engine will produce less thrust than in cold ambient conditions. This will produce a yaw towards the "dead" engine; however, in hot ambient conditions, the ammount of yaw (turning moment) will be reduced and that less rudder will be required to control the aeroplane. In this example, the lowest speed at which you can still control the aeroplane is now reduced, because you will have more rudder available to control the yaw (less thrust from the "live" engine = a reduced turning-moment).
So, Vmca will reduce as ambient temperature increases. Or, if you prefer, Vmca will increase as the ambient temperature decreases... it's the same statement.
Demonstrating Vmca is NOT for the feint-hearted; nor should it be demonstrated by anyone other than a very experienced instructor; also, that he is VERY familiar with the particular aircraft type.
Generally speaking, Vmca will decrease by 1-2 kts per 1000 feet. Also, Vmca will decrease by a similar amount for each 10 degree increase in ambient temperature. Do check your own Pilots Operating Handbook for exact figures.
All of the above is a simplistic method of understanding Vmca. The complexities about whether it's a turbo-charged piston, a normally aspirated engine or a jet engine (or turbo-prop) will only add to your confusion. Keep it simple.
I hope this helps
TCF
Carrying out a Vmca demonstration at 300 feet over the sea is, in my humble oppinion... seeking a death wish!