I guess it's unlikely to be a Naive Entei, but if it was:
Entei @ Life Orb
204 Atk / 128 SpA / 176 Spe Naive
Sunny Day
Flare Blitz
Solarbeam
Stone Edge
With 100% health and a layer of Spikes, you're beating everything on the list 1v1 (with Sunshine) except Aggron and Hariyama. Most of these things are still beaten if you have taken Stealth Rock damage, but you lose your chance to suvive against Regirock. The speed EV's outspeed all Moltres, which means a lot of other stuff, too.
Some Calcs (Itallics for things that are an advantage over Arcanine):
Stone Edge
Moltres: Obviously 100%
Morning Glory Arcanine (-1): 57.5% - 67.8%
Typhlosion: 100%
Ninetales: 100%
Defensive Altaria: 63.3% - 74.6%
Flare Blitz in Sun
Cefable (252 HP / 44 Def): 100%
Chansey (100%)
Umbreon: 78.7% - 92.9%
Physical Tank Hariyama: 37% - 43.7% (solarbeam does slightly more)
Uxie: 57.1% - 67.2%
Crotomb: 76% - 89.8%
Blaziken: 83.7% - 98.7%
Gabite: 96.4% - 113.4%
Sub Punch Aggron: 62.6% - 73.8% (not 2HKO'ed without Sun)
Claydol: 79% - 93.5%
Solarbeam
Milotic: 49.2% - 58.4% (By extension other Bulky Waters are 2HKO'ed with SR as well)
Regirock: 48.4% - 57.1%
Donphan: 92.7% - 109.4%
Cloyster: 96.7% - 114.5%
Very little in UU can switch into Sunny Day and wall this, and few faster things can OHKO it without Stealth Rock. Specs Alakazam does 86.5% - 101.9% with Psychic, which sets the bar pretty well for Special Attacks, considering Sunny Day. LO Dugtrio will do 95.4% - 112.1% so it still risks dying. Both die outright if Entei uses Flare Blitz instead of Sunny Day. Swords Dance Drapion is doing 50-60% with a LO Earthquake and is OHKOed in return. He covers other Fire-types really well; even Bulky Arcanine can be 2HKOed with Stealth Rock. Entei is bulkier against all of these switch-ins than Arcanine is, even with the SpD reducing nature.
Unfortunately, this depends pretty hard on having entry hazards out of the way. Still, a Taunt lead could make it work, since it can break a lot of the walls your opponent sends it's way. Froslass could Taunt your opponent's setup and lay down spikes, possibly even luring in an opposing Fire type for you to set up on.
Also, this may all be wishful thinking because of the nature thing : /.