As with the answer to most things that involves consumption or absorption it's a question of degree, quantity and duration.
Heat is energy that is being transferred.
All life forms require a certain amount of heat to function and survive. Too much heat and not enough heat are detrimental to all life forms.
Applying heat to food by cooking it kills most bacteria associated with the food. Likewise freezing food will initially slow life processes of bacteria and enough cold will also kill many types of bacteria.
As for Earth's environment, if it does not contain enough heat, climate patterns change, ecosystems suffer and the planet freezes, as it has done on a number of occasions when it experienced ice ages. Likewise, with too much heat climate patterns change and ecosystems suffer.
Earth's ecosystem requires a specific range of heat for it to be healthy. This is generally supplied by the Sun but in places can be supplied by the Earth's own geothermal systems, such as volcanic vents, particularly in oceans. Occasional extreme variations in heat can be tolerated if the difference in heat is not too extreme and if the duration of the extreme is short.
Consider the detonation of a thermo-nuclear device in the atmosphere,
the temperatures reached are briefly in the tens of millions of degrees
This is hotter than the Sun and such energy has been released in Earth's environment.
Ignoring the effects of radiation and only considering the heat produced, such detonations product a huge amount of heat for a very short time in a very small region. This adversely affects life forms and the ecosystem in the area of detonation, but the ecosystem recovers from the effect of the heat and the heat does not affect the climate.
If however, there are heat sources covering a large area that is generating a large amount of heat for a prolonged period of time it can affect weather patterns and locally change an ecosystem.
As for the ease of heat exiting Earth's ecosystem it depends on what is in the atmosphere and the proportions of what is in the atmosphere. Cloud cover will retain heat by acting as a blanket. Gases such as methane and carbon dioxide are known for their ability to reflect heat back to the Earth's surface, thus retaining heat in the atmosphere. Increased levels of such gases increases the heat retention within the atmosphere.