Heat is a killer in this game. In the beta you could shut down a Jenner just from jumping max distance for 4 consecutive turns, without firing once. IIRC they turned down heat a little since then but since this is decades before double heatsinks become a thing heat will be an important factor.
* Try to keep the enemy away from rivers and lakes to deny them the heatsink bonus from standing in water. Occupy those points of the map for as long as you can hold them.
* Don't ignore enemy Firestarters just because they have no big guns. Not only are they highly mobile scouts/spotters, their flamers can shut down one of your mechs at the worst possible times.
* Always watch your heat gauge and don't stay in the red for too long. Overheat causes internal damage and can lead to your mech shutting down, thus becoming a sitting duck.
* Consider the heat spike you get from jumping before taking your huge leap to alpha-strike an enemy in the back. You will likely need to cool down in the following round so plan ahead.
* Following up on that keep in mind sprinting increases heat! Not by much but it can be a fatal mistake. I once destroyed my own mech this way when I had it sprint into cover to cool down.