How can a thermometer ever show the actual temperature of an object if the object loses heat to the thermometer? We know that when two objects are placed in contact with each other, after a period of time, the two objects will have the same temperature. Thus, if a hot body comes into contact with a relatively cold body, it will lose its heat and its temperature will reduce, while the temperature of the 'cold' body will increase.
If I put a thermometer in an object to measure its temperature, the body will lose its heat (or gain the heat, if the thermometer is hotter) until it reaches the same temperature as the thermometer. Doesn't this mean the thermometer is not giving us the EXACT temperature of the object, i.e the temperature before the measurement was taken, and is in fact, showing us a lower/higher temperature?
I'll start by mentioning that there's no such thing as an exact measurement—there is always some measurement error.  The only observations that can be numerically exact are counted numbers of discrete objects (e.g., the number of electrons in a neutral carbon atom is exactly 6).  And I say &quot;can be&quot;, because if the numbers are sufficient large, even with counted numbers there can be errors (we see this with vote counting).
Having said that, your idea is correct—if the heat capacity of the temperature probe is significant relative to that of the object being measured, then the measurement can significantly change the temperature of your object.
This is a particular concern when measuring small objects.  For such applications, researchers can employ (as Jon Custer mentioned in his comment) non-contact thermometry.  See, for instance:
https://www.omega.co.uk/temperature/z/noncontacttm.html