Hamish,
Seems logical that would be the case. However, that might be offset by improved air flow and cooling.
When my TR3 was my only ride in the 1960's, I drove it for a year or more with no front grille, until I came up with the few bucks to buy a new one. As I remember, it seemed to run hotter with the new grille. Of course memories from my youth are probably quite unreliable (as are my memories from earlier today).
Tom